Search Site
##### Past 2005 Seminars

 2005 Seminars Time and Date: 10:00 a.m., Wednesday, January 5, 2005 Event: Dept. of Physics & Astronomy Special Talk/Event Speaker:Guifre Vidal, California Institute of Technology Subject:Quantum Information Science and the Efficient Simulation of Quantum Many-Body Systems'' Location:Hennings 318 Time and Date: 2:00 p.m., Wednesday, January 5, 2005 Event: Applied Math/Mathematical Biology Seminar Speaker:Anmar Khadra, Ph.D. Applied Math/Electrical Engineering, University of Waterloo Subject:The Synchronization of Chaos-Generating Systems Using Impulsive Control Techniques with Applications to Communication Security'' Location:WMAX 216 Time and Date: 2:00-3:00 p.m., Thursday, January 6, 2005 Event: Complex Fluids Seminar Speaker:Shreyas Mandre, Department of Mathematics, UBC Subject:TBA'' Location:MATX 1118 Time and Date: 3:00 p.m., Thursday, January 6, 2005 Event: DG-MP-PDE Seminar Speaker:Qinglan Xia, University of Texas at Austin Subject:Ramified phenomena in optimal transportation'' Location:WMAX 216 (PIMS) Time and Date: 3:00 p.m., Friday, January 7, 2005 Event: Mathematics Colloquium Speaker:Qinglan Xia, University of Texas at Austin Subject: The Formation of Tree Leaves'' Location:MATX 1100 Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115). Time and Date:11:00 a.m., Monday, January 10, 2005 Event: Topology Seminar Speaker:Krishnan Shankar, University of Oklahoma Subject:Dehn functions for finitely presented groups'' Location: WMAX 110 (PIMS facility) Time and Date:3:00 p.m., Monday, January 10, 2005 Event: IAM Colloquium Speaker:Neil Balmforth, Earth and Ocean Sciences and Department of Mathematics, UBC Subject:Some Geophysical Roll Waves'' Location:Room 301, Leonard S. Klinck Bldg. Time and Date:4:00 p.m., Monday, January 10, 2005 Event: Mathematics Colloquium Speaker:Katrin Wherheim, Institute for Advanced Study, Princeton University Subject: Floer Theories in Symplectic Topology and Gauge Theory'' Location: MATH 203 Refreshments will be served at 3:45 p.m. in the Faculty Lounge, Math Annex (Room 1115). Time and Date:11:00 a.m., Tuesday, January 11, 2005 Event: DG-MP-PDE Seminar Speaker:Katrin Wherheim, Institute for Advanced Study, Princeton University Subject:Hofer's scale calculus for moduli spaces'' Location: WMAX 110 Time and Date:2:00 p.m., Wednesday, January 12, 2005 Event: Mathematical Biology Seminar Speaker:Fred Brauer, Department of Mathematics, UBC Subject:The Kermack-McKendrick epidemic model revisited'' Location: WMAX 216 Time and Date:3:00 p.m., Wednesday, January 12, 2005 Event: Mathematics Colloquium Speaker:Frank Sottile, Texas A&M University Subject: Tropical Interpolation'' Location: WMAX 110 (PIMS facility) Refreshments will be served at the PIMS Facility prior to the colloquium. Time and Date:2:00-3:00 p.m., Thursday, January 13, 2005 Event: Complex Fluids Seminar Speaker:Shreyas Mandre, Department of Mathematics, UBC Subject:Energy stability of Couette flow'' Location: MATX 1118 Time and Date:3:00 p.m., Thursday, January 13, 2005 Event: Algebra/Topology Seminar Speaker:Dylan Thurston, Harvard University Subject:A random tunnel-number one 3-manifold does not fiber over the circle'' Location: WMAX 216 Time and Date:4:00 p.m., Thursday, January 13, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker:Uli Haussmann, Department of Mathematics, UBC Subject:A stochastic equilibrium economy with irreversible investment, I'' Location: WMAX 216 Time and Date:3:00 p.m., Friday, January 14, 2005 Event: Mathematics Colloquium Speaker:Dylan Thurston, Harvard University Subject: How efficiently do 3-manifolds bound 4-manifolds?'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115). Time and Date:3:00 p.m., Monday, January 17, 2005 Event: IAM Colloquium Speaker:Ozgur Yilmaz, Department of Mathematics, UBC Subject: Blind Separation of Speech Signals via Time-Frequency Masking'' Location: Room 301, Leonard S. Klinck Bldg. Time and Date:4:00 p.m., Monday, January 17, 2005 Event: Mathematics Colloquium Speaker:Patrick Brosnan, SUNY at Buffalo Subject: Motives and the algebraic theory of quadratic forms'' Location: MATH 203 Refreshments will be served at 3:45 p.m. in the Faculty Lounge, Math Annex (Room 1115). Time and Date:4:00-5:00 p.m., Tuesday, January 18, 2005 Event: Algebra/Topology Seminar Speaker:Patrick Brosnan, SUNY at Buffalo Subject:Motivic decompositions arising from the torus method of Bialynicki-Birula'' Location: MATH 203 Time and Date:2:00 p.m., Wednesday, January 19, 2005 Event: Mathematical Biology Seminar Speaker:Dan Luciani, Biophysics & Complex Systems Group, Department of Physics, Technical University of Denmark Subject:Self-sustained and forced oscillations of cytosolic Ca2+ and glucose metabolism in pancreatic islets'' Location: WMAX 216 (PIMS facility) Time and Date:4:00 p.m., Wednesday, January 19, 2005 Event: Probability Seminar Speaker:Nikolai Krylov, University of Minnesota Subject:One more square root law for Brownian motion and its application to SPDEs'' Location: WMAX 216 Time and Date:3:00-4:00 p.m., Thursday, January 20, 2005 Event: DG-MP-PDE Seminar Speaker:Yu Yuan, University of Washington Subject:A Bernstein problem for special Lagrangian equations'' Location: WMAX 110 Time and Date:4:00 p.m., Thursday, January 20, 2005 Event: PIMS-MITACS Math Finance Seminar **CANCELLED** Speaker:Uli Haussmann, Department of Mathematics, UBC Subject:A stochastic equilibrium economy with irreversible investment, II'' Location: WMAX 216 Time and Date:3:00 p.m., Friday, January 21, 2005 Event: Mathematics Colloquium Speaker:Yu Yuan, University of Washington Subject: Fully Nonlinear Elliptic Equations'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115). Time and Date:10:30 a.m., Monday, January 24, 2005 Event: Algebraic Geometry Seminar **Postponed because of visitor's delayed arrival. ** Speaker:Tom Coates, Department of Mathematics, Harvard University Subject:Floer homology, quantization, and Gromov-Witten theory I'' Location:WMAX 110 Time and Date:3:00 p.m., Monday, January 24, 2005 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker:Roger Brockett, Electrical Engineering and Computer Science, Division of Engineering and Applied Sciences, Harvard University Subject:Dynamical Systems that do Tricks'' Location:Room 301, Leonard S. Klinck Bldg. Time and Date:4:00 p.m., Monday, January 24, 2005 Event: Mathematics Colloquium Speaker:Anders Buch, Aarhus Universitet Subject: Quantum cohomology of Grassmannians'' Location:MATH 203 Refreshments will be served at 3:45 p.m. in the Faculty Lounge, Math Annex (Room 1115). Time and Date:10:00 a.m., Tuesday, January 25, 2005 Event: Algebraic Geometry Seminar Speaker:Tom Coates, Harvard University Subject:Floer homology, quantization, and Gromov-Witten theory I'' Location:WMAX 110 Time and Date:11:00 a.m., Tuesday, January 25, 2005 Event: DG-MP-PDE Seminar Speaker:Michael Goldberg, Department of Mathematics, Caltech Subject:A Limiting Absorption Principle in Unweighted L^p Spaces'' Location:WMAX 110 Time and Date:12:30-2:00 p.m., Tuesday, January 25, 2005 Event: SCAIM Seminar Speaker:Brett Gladman, Department of Physics and Astronomy, UBC Subject:Symplectic integrators applied to large-scale dynamical applications in the Solar System'' Location:MATX 1118 Time and Date:4:00-5:00 p.m., Tuesday, January 25, 2005 Event: Problems in Discrete Maths Seminar Speaker:Anders Buch, Aarhus Universitet Subject:Formulas for quiver varieties'' Location:WMAX 216 Time and Date:10:30 a.m., Wednesday, January 26, 2005 Event: Algebraic Geometry Seminar Speaker:Tom Coates, Harvard University Subject:Floer homology, quantization, and Gromov-Witten theory II'' Location:WMAX 110 Time and Date:1:30-2:30 p.m., Wednesday, January 26, 2005 Event: Algebra/Topology Seminar Speaker:Sunil Chebolu, University of Washington Subject:Subcategories and K-theory for Triangulated Categories'' Location:WMAX 110 Time and Date:3:00 p.m., Wednesday, January 26, 2005 Event: Mathematics Colloquium Speaker:Michael Goldberg, Department of Mathematics, Caltech Subject: Dispersive Bounds for the Schrodinger Equation with Almost Critical Potentials'' Location:WMAX 110 Refreshments will be served at 2:45 p.m. in WMAX, Room 101, (the PIMS library). Time and Date:4:00 p.m., Wednesday, January 26, 2005 Event: Probability Seminar Speaker:Nikolai Krylov, University of Minnesota Subject:The Dirichlet problem and diffusion processes in the space of four dimensions more'' Location:WMAX 216 Time and Date:10:00 a.m., Thursday, January 27, 2005 Event: Algebraic Geometry Seminar Speaker:Tom Coates, Harvard University Subject:Floer homology, quantization, and Gromov-Witten theory III'' Location:WMAX 110 Time and Date:3:00-4:00 p.m., Thursday, January 27, 2005 Event: DG-MP-PDE Seminar Speaker:David Ambrose, Courant Institute, New York University Subject:Well-posedness results for water waves and related problems'' Location:WMAX 110 Time and Date:3:00-3:50 p.m., Thursday, January 27, 2005 Event: Number Theory Seminar Speaker:Patrick Ingram, UBC Subject:Integral points on elliptic curves'' Location:UBC Campus, WMAX 216 (PIMS facility) First talk will be followed by a tea break (3:50--4:10 p.m.) Time and Date:4:10-4:35 and 4:35-5:00 p.m., Thursday, January 27, 2005 Event: Number Theory Seminar Speaker:Peter Borwein, SFU Subject:Two problems of Smale that imply a version of P not equal to NP'' and A theorem of Duffin and Shaeffer and related stuff" Location:UBC Campus, WMAX 216 Time and Date:4:00 p.m., Thursday, January 27, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker:Harjoat Bhamra, UBC Finance Subject:The Effect of Financial Innovation on Stock Market Volatility'' Location:WMAX 150 Time and Date:10:30 a.m., Friday, January 28, 2005 Event: Algebraic Geometry Seminar Speaker:Tom Coates, Department of Mathematics, Harvard University Subject:Floer homology, quantization, and Gromov-Witten theory IV'' Location:WMAX 110 Time and Date:3:00 p.m., Friday, January 28, 2005 Event: Mathematics Colloquium Speaker:David Ambrose, Courant Institute, New York University Subject: Analysis and computing for free-surface problems in fluid dynamics'' Location:MATX 1100 Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115). Time and Date:3:00 p.m., Monday, January 31, 2005 Event: IAM Colloquium Speaker:Prof. Robert E. O'Malley, Jr., Department of Applied Mathematics, University of Washington Subject:Using Amplitude Equations to Solve Initial Value Problems over Long Time Intervals'' Location: Room 301, Leonard S. Klinck Bldg. Time and Date:4:00-5:00 p.m., Tuesday, February 1, 2005 Event: Problems in Discrete Maths Seminar Speaker:Josh Cooper, Courant Institute, New York University Subject:Generalized de Bruijn Cycles'' Location: WMAX 216 (PIMS Facility) Time and Date:10:30 a.m., Wednesday, February 2, 2005 Event: Algebraic Geometry Seminar Speaker:Mitja Mastnak, Department of Mathematics, UBC Subject:About Hopf algebra extensions and cohomologies'' Location: WMAX 110 Time and Date:1:30-2:30 p.m., Wednesday, February 2, 2005 Event: Algebra/Topology Seminar Speaker:Nansen Petrosyan, Department of Mathematics, University of Wisconsin-Madison Subject:Groups with periodic cohomology'' Location: WMAX 110 Time and Date:2:00 p.m., Wednesday, February 2, 2005 Event: Mathematical Biology Seminar Speaker:Jonathan Alberts, UW Biology, and Center for Cell Dynamics, FHL Subject:In silico reconstitution of Listeria motility exhibits complex biological behaviors'' Location: WMAX 216 Time and Date:3:00 p.m., Wednesday, February 2, 2005 Event: Mathematics Colloquium Speaker:Josh Cooper, Courant Institute, New York University Subject: Quasirandom Permutations'' Location: WMAX 110 Refreshments will be served at 2:45 p.m. in WMAX, Room 101, (the PIMS library). Time and Date:2:00-3:00 p.m., Thursday, February 3, 2005 Event: Complex Fluids Seminar Speaker:Anthony Huen, Department of Mechanical Engineering, UBC Subject:Stable Multi-layer Visco-plastic Shear Flow'' Location: MATX 1118 Time and Date:3:00 p.m., Thursday, February 3, 2005 Event: DG-MP-PDE Seminar Speaker:Arpad Benyi, Department of Mathematics & Statistics, University of Massachusetts, Amherst Subject:Recent results on bilinear pseudodifferential operators'' Location: WMAX 110 Time and Date:4:00 p.m., Thursday, February 3, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker:Uli Haussmann, Department of Mathematics, UBC Subject:A stochastic equilibrium economy with irreversible investment, II'' Location: WMAX 216 Time and Date:3:00 p.m., Friday, February 4, 2005 Event: Mathematics Colloquium Speaker:Arpad Benyi, Department of Mathematics & Statistics, University of Massachusetts, Amherst Subject: From linear to bilinear pseudodifferential operators'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115). Time and Date:3:00 p.m., Monday, February 7, 2005 Event: IAM Colloquium Speaker:Michael Friedlander, Department of Computer Science, UBC Subject:Solving Quadratic Programs via Gradient Projection'' Location: Room 301, Leonard S. Klinck Bldg. Time and Date:4:00 p.m., Monday, February 7, 2005 Event: Mathematics Colloquium Speaker:Joseph Maher, California Institute of Technology Subject: Geometries and covers of 3-manifolds'' Location: MATH 203 Refreshments will be served at 3:45 p.m. in the Faculty Lounge, Math Annex (Room 1115). Time and Date:12:30-2:00 p.m., Tuesday, February 8, 2005 Event: SCAIM Seminar Speaker:Sarah Mitchell, Department of Mathematics, UBC Subject:An Asymptotic Framework for Finite Hydraulic Fractures driven by Multiple Physical Processes'' Location: MATX 1118 Time and Date:4:00-5:00 p.m., Tuesday, February 8, 2005 Event: Algebra/Topology Seminar Speaker:Joseph Maher, California Institute of Technology Subject:Heegaard splittings and virtual fibers'' Location: West Mall Annex 110 (WMAX - PIMS Facility) Time and Date:4:00-5:00 p.m., Tuesday, February 8, 2005 Event: Problems in Discrete Maths Seminar Speaker:Dimitris Achlioptas, Microsoft Corporation, Redmond, WA Subject:Phase Transitions in Hard Optimization Problems'' Location: WMAX 216 (PIMS Facility) Time and Date:10:30 a.m., Wednesday, February 9, 2005 Event: Algebraic Geometry Seminar Speaker:Angelo Vistoli, Bologna Subject:Chow rings of classifying spaces for classical groups'' Location: WMAX 110 Time and Date:3:00-4:00 p.m., Wednesday, February 9, 2005 Event: Joint Probability-Mathematical Biology Seminar ** Please note special time and location. ** Speaker:Babak Pourbohloul, BC Center for Disease Control Subject:Control of Respiratory-borne disease outbreaks in populations: A Contact Network Theory Approach'' Location: WMAX 110 Time and Date:4:00-5:00 p.m., Wednesday, February 9, 2005 Event: Mathematics Colloquium Speaker:Dimitris Achlioptas, Microsoft Research Subject: Applications of Random Matrices in Spectral Computations and Machine Learning'' Location: WEST MALL ANNEX (WMAX) 110 Refreshments will be served at 3:45 p.m. in WMAX, Room 101 (the PIMS library). Time and Date:10:00 a.m., Thursday, February 10, 2005 Event: Algebraic Geometry Seminar Speaker:Megumi Harada, Department of Mathematics, University of Toronto Subject:Computation of generalized equivariant cohomologies of Kac-Moody flag varieties'' Location: WMAX 110 Time and Date:2:00-3:00 p.m., Thursday, February 10, 2005 Event: Complex Fluids Seminar Speaker:Pramond Patil, Department of Chemical & Biological Engineering, UBC Subject:PTFE Paste Extrusion: Modeling using a Structural Parameter'' Location: MATX 1118 Time and Date:3:00-3:50 p.m., Thursday, February 10, 2005 Event: Number Theory Seminar Speaker:Ron Ferguson, PIMS Subject:The merit factor problem for binary sequences'' Location: SFU Campus, Room K9509 First talk will be followed by a tea break (3:50--4:10 p.m.) Time and Date:4:10-5:00 p.m., Thursday, February 10, 2005 Event: Number Theory Seminar Speaker:Nike Vatsal, Department of Mathematics, UBC Subject:Elliptic curves and modular forms'' Location: SFU Campus, Room K9509 Time and Date:4:00 p.m., Thursday, February 10, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker:Abel Cadenillas, Dept. of Mathematical & Statistical Sciences, University of Alberta Subject:Classical and impulse control for the optimization of the risk and dividend policy of a financial corporation'' Location: WMAX 216 Time and Date:4:00 p.m., Thursday, February 17, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker:Ronnie Sircar, ORFE Department, Princeton University Subject: Valuation of Employee Stock Options'' Location: WMAX 216 Time and Date:3:00 p.m., Monday, February 21, 2005 Event: IAM Seminar Speaker:Mark Martinez, Department of Chemical and Biological Engineering, UBC Subject:An Introduction into the Mathematics of Papermaking'' Location: Room 301, Leonard S. Klinck Bldg. Time and Date:11:00 a.m., Tuesday, February 22, 2005 Event: DG-MP-PDE Seminar Speaker:Evar Ekeland, PIMS, UBC Subject:Regularity in an unusual variational problem'' Location: WMAX 110 (PIMS Facility) Time and Date:12:30-2:00 p.m., Tuesday, February 22, 2005 Event: SCAIM Seminar Speaker:Ian Mitchell, Computer Science, UBC Subject:A Toolbox of Hamilton-Jacobi Solvers for Analysis of Nondeterministic Continuous and Hybrid Systems, and for Dynamic Implicit Surfaces'' Location: FSC 1611 (south side of Forestry Bldg. main floor) Time and Date:4:00-5:00 p.m., Tuesday, February 22, 2005 Event: Problems in Discrete Maths Seminar Speaker:Malek Abdesselam, Department of Mathematics, UBC Subject:Feynman diagrams, classical invariant theory, resultants, and the Hadamard-Foulkes-Howe conjecture'' Location: WMAX 216 Time and Date:10:30 a.m., Wednesday, February 23, 2005 Event: Algebraic Geometry Seminar Speaker:Julianna Tymoczko, U. of Michigan, Ann Arbor Subject:Generalizing group exponents using the topology of subvarieties of the flag variety'' Location: WMAX 110 Time and Date:1:30-2:30 p.m., Wednesday, February 23, 2005 Event: Algebra/Topology Seminar Speaker:Jeffrey H. Smith, Purdue University Subject:The homotopy theory of the Alperin conjecture'' Location: WMAX 110 Time and Date:2:00 p.m., Wednesday, February 23, 2005 Event: Mathematical Biology Seminar Speaker:Colin Clark, Professor Emeritus, Department of Mathematics, UBC Subject:A potpourri of Fishy Models'' Location: WMAX 216 Time and Date:3:00 p.m., Wednesday, February 23, 2005 Event: Mathematics Colloquium Speaker:Sergei Krutelevich, Department of Mathematics & Statistics, University of Ottawa Subject: Jordan algebras, exceptional groups, and higher composition laws'' Location: WMAX 110 (PIMS Facility) Refreshments will be served at 2:45 p.m. in WMAX, Room 101, (the PIMS library). Time and Date:4:15 p.m. (Pls note special time.), Wednesday, February 23, 2005 Event: Probability Seminar Speaker:Alain-Sol Sznitman, ETH Zurich Subject:On random walks in random environment'' Location: WMAX 216 Time and Date:2:00 p.m. (Pls note special time.), Thursday, February 24, 2005 Event: Joint Complex Fluids-SCAIM Seminar Speaker:Guido Kanschat, Applied Mathematics, U. Heidelberg Subject:Discontinuous Galerkin Methods for Incompressible Flow'' Location: MATX 1118 Time and Date:4:00 p.m., Thursday, February 24, 2005 Event: Algebra Seminar Speaker:Sergei Krutelevich, University of Ottawa Subject:The Freudenthal construction and orbits of exceptional groups'' Location: WMAX 216 Time and Date:4:00 p.m., Thursday, February 24, 2005 Event: Graduate Student Seminar Speaker:Yinan Song, Department of Mathematics, UBC Subject:Gromov-Witten/Donaldson-Thomas correspondence'' Location: MATX 1102 Time and Date:4:00 p.m., Thursday, February 24, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker:Anthony Ware, Department of Mathematics, University of Calgary Subject:Natural gas option pricing under mean-reverting price models'' Location: WMAX 110 (Please note the exceptional location.) Time and Date:3:00 p.m., Friday, February 25, 2005 Event: Mathematics Colloquium Speaker:Jeffrey H. Smith, Purdue University Subject: A Tour of the Homotopy Category'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115). Time and Date:3:00 p.m., Monday, February 28, 2005 Event: IAM Seminar Speaker:Robert Bridson, Department of Computer Science, UBC Subject:Animating Fluids'' Location:Room 301, Leonard S. Klinck Bldg. Time and Date:4:00-5:00 p.m., Tuesday, March 1, 2005 Event: Problems in Discrete Maths Seminar Speaker:Richard Anstee, Department of Mathematics, UBC Subject:Some new and interesting results in matching theory'' Location:WMAX 216 Time and Date:1:30-2:30 p.m., Wednesday, March 2, 2005 Event: Algebra/Topology Seminar Speaker:Alejandro Adem, PIMS, UBC Subject:Toroidal Orbifolds and Group Cohomology'' Location:WMAX 110 Time and Date:3:30 p.m., Wednesday, March 2, 2005 Event: Probability Seminar Speaker:Alain-Sol Sznitman, ETH Zurich Subject:Invariance principle and isotropic diffusions in random environment'' Location:WMAX 216 Time and Date:2:00-3:00 p.m., Thursday, March 3, 2005 Event: Complex Fluids Seminar Speaker:Juha Salmela, Pulp and Paper Center, UBC Subject:Floc Rupture and Re-Flocculation in Turbulent Shear Flow'' Location:MATX 1118 Event: 3:00-3:50 p.m., Thursday, March 3, 2005 Time and Date:Number Theory Seminar Speaker:Brian Conrad, University of Michigan Subject:Irreducible specialization in characteristic 2'' Location:UBC Campus, WMAX 110 (PIMS Facility) Time and Date:4:00 p.m., Thursday, March 3, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker:Alexander Melnikov, Department of Mathematics, U. of Alberta Subject:Quantile Hedging and Valuation of equity-linked life insurance contracts'' Location:WMAX 216 Time and Date:3:00 p.m., Friday, March 4, 2005 Event: Mathematics Colloquium Speaker:Alain-Sol Sznitman, ETH Zurich Subject: Random motions in random media'' Location:MATX 1100 Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115). Time and Date:3:30 p.m., Friday, March 4, 2005 Event: SCAIM Seminar Speaker:James Burke, Department of Mathematics, U. of Washington Subject:The Blondel Belgian Chocolate Prize for Polynomial Stabilization: Insights from Nonsmooth Optimization'' Location:UBC Robson Square, Room C225 Time and Date:3:00-4:00 p.m., Monday, March 7, 2005 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker:Adrian Nachman, Department of Mathematics and Department of Electrical & Computer Engineering, U of Toronto Subject:Inverse Problems in Medical Imaging'' Location: Room 301, Leonard S. Klinck Bldg. Time and Date:11:00 a.m., Tuesday, March 8, 2005 Event: DG-MP-PDE Seminar Speaker:Xiaodong Yan, Michigan State University Subject:An example in 2D nonlinear elasticity'' Location: West Mall Annex 110 (PIMS Facility) Time and Date:3:30 p.m., Tuesday, March 8, 2005 Event: DG-MP-PDE Seminar Speaker:Fengbo Han, Michigan State University Subject:The Sobolev inequality for Paneitz operator on Berger spheres'' Location: WMAX 110 Time and Date:4:00-5:00 p.m., Tuesday, March 8, 2005 Event: Problems in Discrete Maths Seminar Speaker:Matthew Morin, UBC Subject:The chormatic symmetric function of caterpillars'' Location: WMAX 216 Time and Date:10:30 a.m., Wednesday, March 9, 2005 Event: Algebraic Geometry Seminar Speaker:Nils Bruin, SFU Subject:The arithmetic of Prym varieties in genus 3 (with applications to finding the rational points on curves)'' Location: WMAX 110 Time and Date:2:00 p.m., Wednesday, March 9, 2005 Event: Mathematical Biology Seminar Speaker:Artem Cherkasov, Division of Infectious Diseases, Faculty of Medicine, UBC Subject:Reliability and network analysis in genomics'' Location: WMAX 216 Time and Date:3:30 p.m., Wednesday, March 9, 2005 Event: Probability Seminar Speaker:Richard Bass, Department of Mathematics, U of Connecticut Subject:Renormalized self-intersection local time and the range of random walks'' Location: WMAX 216 Time and Date:4:00 p.m., Thursday, March 10, 2005 Event: Graduate Student Seminar Speaker:Mathew Rogers, Department of Mathematics, UBC Subject:Bessel functions and infinite series'' Location: MATX 1102 Time and Date:4:00 p.m., Thursday, March 10, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker:Sebastian Ferrando, Ryerson University Subject:Martingales and Wavelets: Applications to Hedging Financial Derivatives'' Location: WMAX 216 Time and Date:3:00 p.m., Friday, March 11, 2005 Event: Mathematics Colloquium Speaker:Richard Bass, University of Connecticut Subject: Jump processes: some links with analysis and PDE'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115). Time and Date:1:00-2:30 p.m., Monday, March 14, 2005 Event: UBC Department of Linguistics sponsored Seminar Speaker:Chung-chieh Shan, Department of Computer Science, Harvard University Subject:Linguistic side effects'' Location: The Buchanan Penthouse, BUCH B 500 (Access is via the SE 4th Flr. Landing.) Time and Date:3:00-4:00 p.m., Monday, March 14, 2005 Event: IAM Seminar Speaker:Anthony Peirce, Department of Mathematics, UBC Subject:Hydraulic Fracture: Multiscale Processes and Moving Interfaces'' Location:Room 301, Leonard S. Klinck Bldg. Time and Date:11:00 a.m., Tuesday, March 15, 2005 Event: DG-MP-PDE Seminar Speaker:Michael Lacey, Georgia Tech Subject:Commutators in Several Parameters'' Location:West Mall Annex 110 (PIMS Facility) Time and Date:11:30 a.m., Tuesday, March 15, 2005 Event: Computer Science Seminar Speaker:Chung-chieh Shan, Department of Computer Science, Harvard University Subject:Meanings are programs with side effects'' Location: FSC 1003 (Forest Sciences Centre) Time and Date:12:30 p.m., Tuesday, March 15, 2005 Event: SCAIM Seminar Speaker:David Watkins, Mathematics, Washington State University Subject:Product Eigenvalue Problems'' Location:FSC 1611 Time and Date:4:00-5:00 p.m., Tuesday, March 15, 2005 Event: Problems in Discrete Maths Seminar Speaker:Shlomo Hoory, Computer Science, UBC Subject:Simple permutations mix well'' Location:WMAX 216 Time and Date:10:30 a.m., Wednesday, March 16, 2005 Event: Algebraic Geometry Seminar Speaker:Kevin Purbhoo, Department of Mathematics, UBC Subject:A Nullstellensatz for Amoebas'' Location:WMAX 110 Time and Date:1:30-2:30 p.m., Wednesday, March 16, 2005 Event: Algebra/Topology Seminar Speaker:Johann Leida, University of Wisconsin Subject:Homotopy Theory of Orbifolds I'' Location:WMAX 110 Time and Date:2:00 p.m., Wednesday, March 16, 2005 Event: Mathematical Biology Seminar Speaker:Jens Rademacher, Department of Mathematics, UBC Subject:Global bifurcations, spectra and dynamics of travelling waves'' Location:WMAX 216 Time and Date:3:30 p.m., Wednesday, March 16, 2005 Event: Probability Seminar Postponed 1 week til March 23rd. Speaker:Alex Roitershtein, Department of Mathematics, UBC Subject:On multi-type branching processes with immigration in random environment'' Location:WMAX 216 Time and Date:2:00-3:00 p.m., Thursday, March 17, 2005 Event: Complex Fluids Seminar Speaker:Markus Weiler, Departments of Forest Resources Management and Geography, UBC Subject:Blue water in macropores'' Location:MATX 1118 Time and Date:3:00 p.m., Thursday, March 17, 2005 Event: DG-MP-PDE Seminar Speaker:Louis Nirenberg, NYU Subject:A geometric problem and its connection to the Hopf lemma'' Location:WMAX 110 Time and Date:3:00-3:50 p.m., Thursday, March 17, 2005 Event: Number Theory Seminar Speaker:Michael Rubinstein, University of Waterloo Subject:Elliptic curves and random matrix theory'' Location:SFU Campus, Room K9509 Tea break: 3:50 - 4:10 p.m. Time and Date:4:10-5:00 p.m., Thursday, March 17, 2005 Event: Number Theory Seminar Speaker:Chandrashekhar Khare, University of Utah Subject:Serre's conjectures on mod p Galois representations'' Location:SFU Campus, Room K9509 Time and Date:4:00 p.m., Thursday, March 17, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker:Ivar Ekeland, PIMS, UBC Subject:On Bond Prices'' Location:WMAX 216 Time and Date:3:00 p.m., Friday, March 18, 2005 Event: Mathematics Colloquium Speaker:Sara Billey, University of Washington Subject: Intersecting Schubert Varieties'' Location:MATX 1100 Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115). Time and Date:11:00 a.m., Tuesday, March 29, 2005 Event: DG-MP-PDE Seminar Speaker: Jerome Demange, Toulouse Subject:Porous Media Equation and Sobolev Inequalities on Manifolds'' Location: West Mall Annex (WMAX) 110 (PIMS Facility) Time and Date:4:00-5:00 p.m., Tuesday, March 29, 2005 Event: Problems in Discrete Maths Seminar Speaker: Roger Woodford Subject:Prime Symmetric Divisor Functions'' Location: WMAX 216 Time and Date:10:30 a.m., Wednesday, March 30, 2005 Event: Algebraic Geometry Seminar Speaker: Mike Roth, Queen's Subject:Stable Maps and Quot Schemes'' Location: WMAX 110 Time and Date: 1:30 p.m., Wednesday, March 30, 2005 (Please note 1/2 hr earlier than usual) Event: Mathematical Biology Seminar Speaker: Gustavo Carrero, Department of Mathematics, University of Alberta Subject:Modelling the Compartmentalization of Splicing Factors'' Location: WMAX 216 Time and Date:3:00-4:00 p.m., Wednesday, March 30, 2005 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: Raymond Pierrehumbert, Department of Geophysical Sciences, University of Chicago Subject:Early-Life Crises of Habitable Planets'' Location: Room 301, Leonard S. Klinck Bldg. Time and Date:3:30 p.m., Wednesday, March 30, 2005 Event: Probability Seminar Speaker: John Walsh, Department of Mathematics, UBC Subject:Some Remarks on the Numerics of the Nonlinear Stochastic Wave Equation'' Location: WMAX 216 Time and Date: 1:00 p.m., Thursday, March 31, 2005 Event: Special Probability Seminar Speaker: Jeremy Flowers Subject:Hydrodynamical Scaling Limits of Simple Exclusion Processes'' Location: MATX 1118 Time and Date: 4:00 p.m., Thursday, March 31, 2005 Event: Graduate Student Seminar Speaker: Izak Grguric, Department of Mathematics, UBC Subject:Equivariant Cobordism'' Location: MATX 1102 Time and Date:  4:00 p.m., Thursday, March 31, 2005 Event:  PIMS-MITACS Math Finance Seminar Speaker:  Ulrich Horst, Department of Mathematics, UBC Subject:  "Non-Ergodic Stock Price Dynamics in a CAPM with Interacting Agents" Location: WMAX 216   Time and Date:3:00 p.m., Monday, April 4, 2005 Event: Special Probability Seminar Speaker:Jeremy Flowers, Department of Mathematics, UBC Subject:Hydrodynamical Scaling Limits of Simple Exclusion Processes II'' Location: MATX 1102 Time and Date:11:00 a.m., Tuesday, April 5, 2005 Event: DG-MP-PDE Seminar Speaker:Tai-Peng Tsai, Department of Mathematics, UBC Subject:Stability in H^1 of the sum of K solitary waves for some nonlinear Schrodinger equations'' Location: WMAX 110 Time and Date:12:30 p.m., Tuesday, April 5, 2005 Event: SCAIM Seminar Speaker:Pengtao Yue & Chunfeng Zhou, Chemical & Biological Engineering, UBC Subject:A Finite-Element Diffuse-Interface Method for Interfacial Flows with Adaptive Meshing'' Location: MATX 1118 Time and Date:2:00 p.m., Wednesday, April 6, 2005 Event: Mathematical Biology Seminar Speaker:Adriana Dawes, Department of Mathematics, UBC Subject:Modelling the spatial profile of barbed ends and filament density behind the leading edge of a motile cell'' Location: WMAX 216 Time and Date:3:00 p.m., Wednesday, April 6, 2005 Event: Algebraic Geometry Seminar Speaker:Alexander Yong, Berkeley Subject:On Smoothness and Gorensteinness of Schubert varieties'' Location: WMAX 110 Time and Date:3:30 p.m., Wednesday, April 6, 2005 Event: Probability Seminar Speaker:Ulrich Horst, Department of Mathematics, UBC Subject:State dependent queuing systems with semi-Markov switching and applications to finance'' Location: WMAX 216 Time and Date:2:00 p.m., Wednesday, April 13, 2005 Event: Mathematical Biology Seminar Speaker:Christopher Kribs Zaleta, U. Texas, Arlington Subject:Vector consumption and contact process saturation in sylvatic transmission of T. cruzi'' Location:WMAX 216 Time and Date:3:00 p.m., Friday, April 15, 2005 Event: Mathematics Colloquium Speaker:Boris Kunyavskii, Bar Ilan University Subject: Characterization of radicals in finite dimensional Lie algebras and finite groups'' Location:WMAX 110 (PIMS Facility) Refreshments will be served at 2:45 p.m. in the PIMS 1st floor lounge. Time and Date:1:30 p.m., Monday, April 18, 2005 Event: Algebra Topology Seminar Speaker:Hendryk Pfeiffer, Cambridge University Subject:From Hopf algebras to trialgebras and Hopf categories'' Location: WMAX 110 Time and Date:3:00 p.m., Monday, April 18, 2005 Event: Mathematics Colloquium Speaker:R. Sujatha, School of Mathematics, Tata Institute of Fundamental Research Subject: Birational Geometry and localisation'' Location: WMAX 110 (PIMS Facility) Refreshments will be served at 2:45 p.m. in the PIMS 1st floor lounge. Time and Date:2:00 p.m., Wednesday, April 20, 2005 Event: Mathematical Biology Seminar Speaker:Don Ludwig, Emeritus, Department of Mathematics, UBC Subject:Uncertainty in Discount Models and Mitigation of Environmental Change'' Location: WMAX 216 Time and Date:3:00 p.m., Tuesday, April 26, 2005 Event: Algebraic Geometry Seminar Speaker:Behrang Noohi, Max-Planck Institute Subject:Uniformization of Deligne-Mumford curves'' Location:WMAX 110 Time and Date:2:00 p.m., Wednesday, April 27, 2005 Event: Mathematical Biology Seminar Speaker:Amil Shah, MDCM, FRCPC, FACP Medical Oncologist, Vancouver Cancer Centre Subject:In Search of the Achilles Heel of Cancer'' Location:WMAX 216 Time and Date:3:00 p.m., Friday, April 29, 2005 Event: Mathematics Colloquium Speaker:Benny Sudakov, Princeton University Subject: Probabilistic reasoning and Ramsey Theory'' Location:WMAX 110 (PIMS Facility) Refreshments will be served at 2:45 p.m. in the PIMS 1st floor lounge. Time and Date:9:00 a.m.- 6:00 p.m., Friday, June 3, 2005 Event: Foundational Methods in Computer Science (FMCS05) Local organizer: John MacDonald Location:All sessions are held in WMAX 110 - 1933 West Mall. 9:00-10:30a.m. Ernie Manes, U Mass Amherst, USA Subject:From locally-Boolean rings to sum-ordered categories'' 11:00-12:30p.m. Vaughan Pratt, Stanford University, USA Subject:Recent developments in Chu spaces'' 2:30-4:00p.m. Steve Bloom, Stevens Institute of Technology, USA Subject:Regular words'' 4:30-6:00p.m. Robin Cockett, University of Calgary Subject:Restriction Categories and Ehresmann's Theorem'' Time and Date:9:00 a.m.- 5:00 p.m., Saturday, June 4, 2005 Event: Foundational Methods in Computer Science (FMCS05) 9:00-9:50a.m. Paul Taylor, Manchester, UK Subject:Extension of ASD (from locally compact locales) to and beyond general locales'' 9:50-10:30a.m. Cyrus Nourani, USA Subject:Functorial Model Computations'' 11:00-11:30a.m TBA 11:30-12:15p.m. Art Stone, Vancouver, Canada Subject:2-Dimensional Adjunctions'' 2:00-2:30p.m. Varmo Vene, University of Tartu, Estonia Subject:Signals and Comonads'' 2:30-3:00p.m. Bob Rosebrugh, Mt. Allison University Subject:TBA'' 3:00-3:30p.m. Chris Dutchyn, University of British Columbia Subject:Aspects are Dual to Objects'' 4:00-5:00p.m. Philip Mulry, Colgate University, USA Subject:Monad Compositions on Recursive Data Types'' Time and Date:9:00 a.m.- 12:30 p.m., Sunday, June 5, 2005 Event: Foundational Methods in Computer Science (FMCS05) 9:00-9:30a.m. Brian Redmond, University of Ottawa Subject:Categorical Models for Soft Linear Logic'' 9:30-10:00a.m. X. Guo, University of Calgary Subject:Range Restriction Categories'' 10:00-10:30a.m. Dana Harrington, University of Calgary Subject:TBA'' 10:30-11:00a.m. Break 11:00-11:30a.m. David Oury, McGill University Subject:TBA'' 11:30-12:00p.m. Pieter Hofstra, University of Ottawa Subject:TBA'' 12:00-12:30p.m. TBA Last updated: 5/27/05 Time and Date: 4:00-5:00 p.m., Thursday, June 16, 2005 Event: Probability Seminar Speaker:Thomas Duquesne, ENS, Paris Subject:Brownian and Levy Continuum Random Trees'' Location:West Mall Annex 110 (Coffee will be served at 3:30 p.m. in the 1st floor PIMS Lounge.) Time and Date: 3:30 - 4:30 p.m., Wednesday, August 31, 2005 Event: Probability Seminar Speaker: Stanislav Volkov, U. Bristol, UK Subject:5x+1: how many go down?'' Location: West Mall Annex Room 216, 1933 West Mall, PIMS Facility Abstract: I will talk about how probabilistic methods of analyzing randomly-labeled trees can provide an important insight on the 5x+1 version of the famous Collatz problem (3x+1), you might have a look at http://mathworld.wolfram.com/CollatzProblem.html (Mathworld). Though no rigorous results about number theory will be proved in my talk, a number of properties of the trees with random labels will be rigorously established. Time and Date:11:00 a.m., Wednesday, September 7, 2005 Event: Algebraic Geometry Seminar Subject:Organizational Meeting Location:West Mall Annex, Room 110, 1933 West Mall, PIMS Time and Date:2:00 p.m., Wednesday, September 7, 2005 Event: Mathematical Biology Seminar Speaker:Lindi Wahl, U of Western Ontario Subject:Modelling Experimental Evolution'' Location:West Mall Annex, Room 216, 1933 West Mall, PIMS Abstract: In experimental evolution, populations of microbes are grown under laboratory conditions for thousands of generations -- enough time for significant evolutionary change to occur. The results of these experiments in the past several years have shed enormous light on the trajectories and outcomes of evolution. In parallel with this experimental effort, we have developed mathematical models of experimental evolution, deriving in particular the probability that rare, beneficial mutations will emerge and invade the population. I will give an overview of our techniques and results to date, highlighting some interesting predictions of the model. For example, we derive an optimal dilution ratio, that is, the length of time populations should be allowed to grow in order to maximize the rate of evolution. In addition, we predict that mutations which allow the microbe to reproduce more quickly, as opposed to reproducing more prolifically, are less likely to invade. Time and Date:3:30--4:30 p.m., Wednesday, September 7, 2005 Event: Probability Seminar Speaker:Gord Slade, Department of Mathematics, UBC Subject:The survival probability for critical oriented percolation above 4+1 dimensions'' Location:West Mall Annex, Room 216 Abstract: We consider spread-out critical oriented percolation in d + 1 dimensions. We develop a new point-to-plane version of the lace expansion and use it to prove that the probability that the cluster of the origin survives to time n is asymptotic to a multiple of n^{-1}, when d is greater than 4. This is joint work with Remco van der Hofstad and Frank den Hollander. Time and Date:3:30--4:20 p.m., Thursday, September 8, 2005 Event: DG-MP-PDE Seminar Speaker:Tetsu Mizumachi, Kyushu University Subject:Instability of vortex solitons for 2D focusing NLS'' Location:West Mall Annex, Room 110 Abstract: We consider standing wave solutions e^{i(m\theta+\omega t)}\phi_{\omega,m}(r) to iu_t+\Delta u+|u|^{p-1}u=0,\quad\text{for x\in\R^2, t>0,} where m\in\N and (r,\theta) are polar coordinates in \R^2. We investigate a limiting profile of \phi_{\omega,m} as m\to\infty and show that for every p>1 the standing wave solutions are unstable for large m. Time and Date:4:00--5:00 p.m., Thursday, September 8, 2005 Event: Math Finance Seminar Speaker:Matthias Mueller, Department of Mathematics, UBC Subject:Pricing and hedging market external risks: weather and climate'' Location:West Mall Annex, Room 216 Abstract: Weather and climate risks can not be hedged on stock markets. Those risk factors are market external. The utility indifference pricing approach does not give satisfying results because the market is too incomplete. Our approach is the completion of the market by a risk bond. This risk bond makes the external risk tradable. In presence of an exogenously given stock market, a fixed point argument yields the price for the external risk factor. If the preferences of the economic agents are described by exponential utility, the market price of external risk is defined by a Backward Stochastic Differential Equation. In Markovian models, this BSDE can be transformed into a quasilinear PDE. Simulations of toy models give some insight in prices and hedging strategies. Time and Date:3:00 p.m., Friday, September 9, 2005 Event: Mathematics Colloquium Speaker:Mike Bennett, Department of Mathematics, UBC Subject: Diophantine Equations, Old and New'' Location:MATX 1100 Refreshments will be served at 2:45 p.m. (MATX 1115, Faculty Lounge). Time and Date:2:00--3:00 p.m., Monday, September 12, 2005 Event: Algebra Topology Seminar Speaker:Antonio Ramirez, Department of Mathematics, UBC Subject:String Topology'' Location:West Mall Annex, Room 216 (PIMS) Note: We will have a short organizational meeting before the talk. Anyone who is interested in the seminar but cannot make this meeting should send Laura Scull an e-mail. Time and Date:3:00 p.m., Monday, September 12, 2005 Event: IAM Seminar Series Speaker:Michael Doebeli, Zoology, Mathematics, IAM, UBC Subject:The Steacie Fellowship Prize Lecture: Evolution and Diversity'' Location:Room 301, Leonard S. Klinck Bldg. Abstract: Understanding the origin of diversity is a fundamental problem in biology. Traditional evolutionary theory predicts uniformity: acting on organisms under given environmental conditions and developmental constraints, natural selection produces a unique, optimally adapted phenotype. According to this view, different types only come about through a change in conditions over space or time. In particular, the process of diversification, that is, the split of an ancestral population into distinct descendent lineages, is a by-product of geographical separation. This traditional view misses out on the important perspective that diversification itself can be an adaptive process. In this talk I will review recent theoretical work showing that diversification as an adaptive response to biological interactions is a plausible evolutionary process. This work is based on the mathematical framework of adaptive dynamics, and in particular on the phenomenon of evolutionary branching due to frequency-dependent ecological interactions. I will describe evolutionary branching in a number of different models, including models for competitive and for cooperative interactions. I will also describe ongoing efforts to test the theory of evolutionary branching in evolving Escherichia coli populations, which provide a promising experimental model system for studying adaptive diversification. Time and Date:3:00--4:00 p.m., Monday, September 12, 2005 Event: Algebraic Geometry Seminar Speaker:Jim Bryan, UBC Subject:Hurwitz-Hodge integrals and the Crepant Resolution Conjecture'' Location:West Mall Annex, Room 110 (PIMS) Abstract: A well known principle from physics states that string theory on an orbifold X is equivalent to string theory on Y, any crepant resolution of X. In mathematics, this can be stated as saying that the Gromov-Witten potentials for X and Y contain equivalent information. I will illustrate this in some simple examples and show how it leads to interesting new formulas for integrals of Hodge classes over Hurwitz schemes. Time and Date:12:30 p.m., Tuesday, September 13, 2005 Event: SCAIM Seminar Speaker:Ping Lin, Department of Mathematics, National University of Singapore Subject:A quasi-continuum approximation for material problems and its analysis'' Location:Math Annex 1118 Abstract: In many applications materials are modeled by a large number of particles (or atoms) where any one of particles interacting with all others through a (nonconvex) pair potential energy. The equillibrium configuration of the material is the minimizer of the total energy of the system. The computational cost is very high since the number of atoms is huge. Recently much attention has been paid to a so-called quasicontinuum (QC) method which is a mixed atomistic/continuum model. The QC method solves a fully atomistic problem in regions where the material contains defects (or larger deformation gradients), but uses continuum finite elements to effectively integrate out the majority of the atomistic degrees of freedom in regions where deformation gradients are small. However, numerical analysis is still at its infancy. In this talk we will conduct a convengence analysis of the QC method in the case that there is no defect or that the defect region is small. The difference of our analysis from conventional one is that our exact solution is not a solution of a continuous partial diffeeential equation but a discrete lattice scale solution which is not related to any conventional partial differential equation. We will consider both one dimensional and two dimensional cases. The talk may be related to some other fields such as model reduction and pre-conditioning. Pizza and pop served, as usual. Time and Date:3:30--4:30 p.m., Tuesday, September 13, 2005 Event: Joint SFU/UBC Discrete Math/CS Theory Seminar Speaker:Gabor Tardos, Simon Fraser University Subject:Toward an Extremal Theory of Ordered Graphs'' Location:West Mall Annex, Room 216 (PIMS at UBC) Abstract: Pattern avoidance raises very interesting extremal enumerative and structural problems in many different contexts from Turan-type extremal graph theory to Davenport-Schinzel theory. This survey talk concentrates to 0-1 matrices and (the closely related concepts of) ordered graphs. An ordered graph is simple graph together with a linear order on its vertices. Time and Date:2:45--3:35 p.m., Wednesday, September 14, 2005 Event: PIMS Afternoon Tea Location:West Mall Annex, Room 101 (PIMS Library) Time and Date:3:30--4:30 p.m., Wednesday, September 14, 2005 Event: Probability Seminar Speaker:Alan Hammond, Department of Mathematics, UBC Subject:Mass-conservation and gelation in reaction-diffusion PDE'' Location:West Mall Annex, Room 216 Abstract: Smoluchowski's coagulation equation is a PDE that models the changing densities of a system of mass bearing particles that diffuse and are liable to coagulate in pairs at close range. We analyse the behaviour of solutions of the PDE by monitoring the trajectory of a tracer particle, this particle diffusing in space and colliding with other particles in accordance with the densities provided by a given solution of the PDE. We prove uniform bounds on the total particle density under certain assumptions on the parameters that specify the PDE. These permit us to derive conditions under which the solutions conserve mass for all time. In the other case, a gelation phenomenon occurs, much like a phase transition. Time permitting, I will also discuss results proving that gelation occurs. Time and Date:4:00--5:00 p.m., Thursday, September 15, 2005 Event: Math Finance Seminar Speaker:Matthias Mueller, Department of Mathematics, UBC Subject:Pricing and hedging market external risks: weather and climate -- Open Problems'' Location:West Mall Annex, Room 216 Time and Date:4:00--5:30 p.m., Thursday, September 15, 2005 Event:Complex Fluids Seminar Speaker:Pramod D. Patil, Department of Chemical and Biological Engineering, UBC Subject:Microstructural modeling and flow simulations of PTFE paste extrusion'' Location:MATH 225 Abstract: Because of its high melt viscosity, polytetrafluoroethylene (PTFE) is usually processed by paste extrusion instead of conventional melt processing techniques. Experimentally it has been reported that the extrusion pressure varies non-monotonically with the entrance angle of the conical die attached at the bottom of a capillary extruder. SEM micrographs show the formation of submicron-diameter fibrils in between polymer particles due apparently to squeezing of neighboring particles inside the converging conical die and unwinding of mechanically locked crystallites. In the present study the mechanism of fibrillation is captured through a microscopic model for a structural parameter that accounts for the population of fibrils. The evolution of the structural parameter is described by a first-order kinetic differential equation. A constitutive equation is constructed that shows shear-thinning and shear-thickening behavior depending on the evolution of the structural parameter during extrusion. Finite element simulations have predicted variations of the extrusion pressure with the apparent shear rate and die geometry, especially the die entrance angle. The simulation results will be compared with experimental findings. Key words: PTFE paste, extrusion, conical die, fibrils, micro-structural parameter, shear thinning, Shear thickening, finite element simulations Time and Date:3:00 p.m., Friday, September 16, 2005 Event: Mathematics Colloquium Speaker:Alexander Holroyd, Department of Mathematics, UBC Subject: The Bootstrap Percolation Cellular Automaton -- a case study in Theory versus Experiment'' Location:MATX 1100 Refreshments will be served at 2:45 p.m. (MATX 1115, Faculty Lounge). Time and Date:3:00--4:00 p.m., Monday, September 19, 2005 Event: IAM Seminar Series Speaker:Michael Ward, Department of Mathematics, UBC Subject:The Stability of Stripes, Rings, and Spots, in some Reaction-Diffusion Systems'' Location:Room 301, Leonard S. Klinck Bldg. Abstract: Stripe or ring patterns have been observed in many numerical simulations of singularly perturbed reaction-diffusion systems. They occur for activator-inhibitor systems such as the well-known Gierer-Meinhardt model of biological morphogenesis, for certain hybrid chemotaxis reaction-diffusion systems modeling fish skin patterns on growing domains, and for the Gray-Scott system of theoretical chemistry. In many instances a stripe or ring pattern is unstable to a breakup instability, which leads to the disintegration of the stripe or ring into a sequence of spots. In other cases, a stripe is de-stabilized by a transverse or zigzag instability, leading to a wriggled stripe. In certain cases, this wriggled stripe is the precursor to a complicated space-filling labyrinthian pattern. Most previous studies of this phenomenon are based on a weakly nonlinear theory near some spatially uniform steady-state. In contrast, the stripes that we consider are typically localized along some planar curves and have cross-sections that deviate substantially from the background state. The cross-sections are either homoclinic or front-back transition solutions of certain ODE systems. Our analysis of stripe stability involves a combination of singular perturbation theory, the spectral theory of nonlocal eigenvalue problems, and numerical computations. The instabilities of these localized stripes are illustrated for various reaction-diffusion models, and some general results are given for the occurrence of spot-generating instabilities, zigzag instabilities, and labyrinthian patterns. This is joint work with Theodore Kolokolnikov, Wentao Sun, and Juncheng Wei. Time and Date:3:00--4:00 p.m., Monday, September 19, 2005 Event: Algebraic Geometry Seminar Speaker:Hsian-Hua Tseng, Department of Mathematics, UBC Subject:Bend and break: old and not-so-old'' Location:West Mall Annex, Room 110 (PIMS) Abstract:"Bend and break" was introduced by S. Mori as a way to produce rational curves on smooth projective varieties. The method was further developed by J. Kollar for singular varieties. In this talk we'll review this technique for smooth varieties. We'll then discuss a different approach to extend it to singular varieties (joint work with Jiun-Cheng Chen). Time and Date:12:30 p.m., Tuesday, September 20, 2005 Event: SCAIM Seminar Speaker:Chen Greif, Department of Computer Science, UBC Subject:Preconditioners for the Time-Harmonic Maxwell Equations in Mixed Form'' (joint work with Dominik Schoetzau, UBC) Location:Math Annex 1118 Abstract:We introduce a new preconditioning technique for iteratively solving linear systems arising from finite element discretizations of the mixed formulation of the time-harmonic Maxwell equations, with small wave numbers. The preconditioners are based on augmentation, and are motivated by spectral equivalence properties of the discrete operators. We show that using the scalar Laplacian as a weight matrix works as an effective block diagonal preconditioner, for which fast iterative solution methods can be applied. The analytical observations are accompanied by numerical examples that demonstrate the scalability of the technique. Time and Date:3:30 p.m., Tuesday, September 20, 2005 Event: DG-MP-PDE Seminar Speaker:Stephen Gustafson, Department of Mathematics, UBC Subject:Scattering for the Gross-Pitaevskii equation'' Location:West Mall Annex, Room 110 (PIMS) Abstract: The Gross-Pitaevskii equation, a model for Bose-Einstein condensates, superfluids, and superconductors, is just a familiar nonlinear Schroedinger equation, but with a non-zero limit at spatial infinity. This boundary condition makes it a more challenging (and interesting) problem to determine the long-time behaviour of solutions. I'll give some nonlinear scattering background, and describe some results (joint with K. Nakanishi and T.-P. Tsai) and open problems. Time and Date:3:30--4:30 p.m., Tuesday, September 20, 2005 Event: Discrete Math Seminar Speaker:Chris Ryan, Commerce, UBC Subject:Coincidences amongst products of Schur functions'' Location:West Mall Annex, Room 216 (PIMS) Time and Date:2:00 p.m., Wednesday, September 21, 2005 Event: Mathematical Biology Seminar Speaker:Steven Plotkin, Physics and Astronomy, UBC Subject:How does a protein fold? The effects of structure, and a segue into differential geometry'' Location:West Mall Annex, Room 216 Abstract:The elusive theory for how a protein folds up to a biologically functional structure has occupied researchers for the last few decades. The difficulties stem from an incomplete knowledge of an accurate Hamiltonian, as well as non-trivial aspects of polymer physics that complicate the kinetics of folding. Here I will describe some recent results showing that relaxation rates increase significantly as the folding mechanism becomes increasingly heterogeneous. A search for a suitable reaction coordinate leads to an unsolved problem in differential geometry, namely a precise mathematical formulation of distance between objects of dimension > 0. A distance metric for two non-crossing space curves can be formulated as a variational problem, mapping to the solution of a partial differential equation. I will describe these developments and discuss some possible future directions. Time and Date:2:45--3.35 p.m., Wednesday, September 21, 2005 Event: PIMS Tea Location:West Mall Annex, Room 101 (PIMS Library) Time and Date:3:30 p.m., Wednesday, September 21, 2005 Event: Algebra Topology Seminar Speaker:Antonio Ramirez, Department of Mathematics, UBC Subject:Open-Closed String Topology'' Location:West Mall Annex, Room 110 Abstract: This is a continuation to last week's talk on string topology. I will continue with TQFT aspects of string topology, and describe how the constructions can be extended to the "open closed" setting, in which one considers not only loops but also spaces of paths in M with endpoint conditions given by submanifolds. The method of construction is homotopy theoretic, and it makes use of constrained mapping spaces from certain decorated fat graphs into the ground manifold M. Time and Date:3:30--4:30 p.m., Wednesday, September 21, 2005 Event: Probability Seminar Speaker:David Wilson, Microsoft Research Subject:Random-turn games'' Location:West Mall Annex, Room 216 Abstract: The game of Hex has two players who take turns placing stones of their colors on the hexagons of a rhombus-shaped hexagonal grid. Black wins by completing a crossing between two opposite edges, while White wins by completing a crossing between the other pair of opposite edges. Although ordinary Hex is famously difficult to analyze, random-turn Hex---in which players toss a coin before each turn to decide who gets to place the next stone---has a simple optimal strategy. We describe the optimal strategy and study the expected length of the game under optimal play for random-turn Hex and several other selection games''. We also study another class of random-turn games, called tug-of-war, which is played on a length space X with terminal states at which there is a payoff; the winner of the coin toss may move the current state by up to distance epsilon. Strategies for tug-of-war give a new way to study the infinity-Laplacian. Joint work with Yuval Peres, Oded Schramm, and Scott Sheffield. Time and Date:4:00--5:00 p.m., Thursday, September 22, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker:Dmity Kramkov, Carnegie Mellon University Subject:On the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets'' Location:West Mall Annex, Room 216 Abstract:We study the two-times differentiability of the value functions to the primal and dual optimization problems that appear in the setting of expected utility maximization in incomplete markets. We also study the differentiability of the optimal solutions to these problems with respect to their initial values. We show that the key conditions for the results to hold true are that the relative risk-aversion coefficient of the utility function is uniformly bounded away from zero and infinity and that the prices of traded securities are sigma-bounded under the numeraire given by the optimal wealth process. The presentation is based on a joint paper with Mihai Sirbu. The preprint is available from http://www.math.cmu.edu/~kramkov/publications.html . Time and Date:4:00--5:30 p.m., Thursday, September 22, 2005 Event: Complex Fluids Seminar Speaker:Paul X. Chen, Dept. of Chemical and Biological Engineering, UBC Subject:Drop/Interface Coalescence in Non-Newtonian Liquid'' Location:MATH 225 Abstract: When a water drop falls through oil and comes to rest on an oil-water interface, several interesting phenomena may occur. First, the oil film separating the drop and the water bath underneath is squeezed and gets thinner. The drainage of the film depends on the viscosity of the oil, among other things, and its efficiency, represented by a rest time, varies greatly among different fluids. Second, the coalescence between the drop and the water bath may be arrested before completion if a capillary instability in the neck develops faster than the deflation of the drop. A smaller secondary drop pinches off from the neck and will remain on the interface. This episode, known as partial coalescence, repeats itself several times before the drop finally disappears. In this talk, I will describe experiments designed to explore the role of oil rheology in the above phenomena. In particular, I will present data on rest time, coalescence time, and the reduction of drop size during partial coalescence when polymer is added to the oil phase. Video footage captured with our newly acquired high-speed camera will reveal details of the process. Some of the results are unexpected and unexplained at present. Time and Date:3:00 p.m., Friday, September 23, 2005 Event: Mathematics Colloquium Speaker:Rachel Kuske, Department of Mathematics, UBC Subject: Hidden time scales and stochastic dynamics'' Location:MATX 1100 Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 2:45 p.m., Monday, September 26, 2005 Event: Mathematics Departmental Tea Location: Math Annex 1115 (Math Lounge) Time and Date: 3:00--4:00 p.m., Monday, September 26, 2005 Event: IAM-PIMS-MITACS 2005-2006 Distinguished Colloquium Series Speaker: Eli Tziperman, Department of Earth and Planetary Sciences, Division of Engineering and Applied Sciences, Harvard University Subject:Rapid Past Climate Change: It's the Sea Ice'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Heinrich events are massive glacier discharges from the ice sheets around the North Atlantic Ocean which occurred every 7,000-10,000 years during the last glacial period (10,000-50,000 years ago). Each of these events also triggered an abrupt atmospheric warming of some 10 degrees Celsius around the northern North Atlantic. The warming (Dansgaard-Oeschger event) occurred rapidly, in about twenty years, lasted a few hundred years, and terminated abruptly again, within a few decades. We suggest that such past rapid climate changes during the last glacial maximum have occurred due to rapid sea ice melting and formation. A specific mechanism is proposed for the climatic effects of Heinrich events. The synchronous iceberg discharges from several ice sheets around the North Atlantic are explained by a nonlinear phase locking between the different glaciers. Time and Date: 3:00--4:00 p.m., Monday, September 26, 2005 Event: Algebraic Geometry Seminar Speaker: Michael Thaddeus, Columbia U., PIMS Subject:Stable maps to loop groups'' Location: West Mall Annex, Room 110 (PIMS) Time and Date: 12:30 p.m., Tuesday, September 27, 2005 Event: SCAIM Seminar Speaker: Ofer Levi, Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Israel Subject:Direct and Exact Inverse PPFFT and Radon Transforms Using Orthogonalizing Weights'' Location: Math Annex 1118 Abstract: The Pseudo-Polar FFT (PPFFT), which was developed and presented by Averbuch et. al, computes Discrete Fourier Transform coefficients on a nearly polar grid. The special structural properties of the Pseudo-Polar grid allow a computational complexity of o(n2log(n)) for an n by n image (as opposed to o(n4) in the polar case). Averbuch et. al. also presented a weighted version of the PPFFT that is nearly orthogonal and can be used for the application of an extremely fast iterative inverse solver. The PPFFT is directly related to a highly accurate and fast version of the Discrete Radon Transform that possesses the same desirable computational properties as the PPFFT, the Fast Slant-Stack Transform. In many instances and applications the PPFFT can be a very good substitute for the Polar FT and its superior computational properties can speed up many related algorithms by several orders of magnitude. Classical applications of Polar FFT include rotational registration of images and reconstruction in medical and biological imaging. The preliminary part of this talk will introduce the basics of 2D DFTs in Cartesian, Polar and PP grids using matrices and vectors notation. Later on, a new direct an exact inverse PPFFT will be presented, the algorithm is based on a preprocessing step in which an optimal set of weights is computed for the given image size, these weights perfectly orthogonalize the columns of the transform's matrix so the inverse problem can be solved exactly by a single application of the Adjoint PPFFT which can be computed as well in o(n2log(n)) complexity. The results will be generalized to 3D as well as to radon transforms in 2D and 3D. Time and Date: 3:30 p.m., Tuesday, September 27, 2005 Event: DG-MP-PDE Seminar Speaker: Hadi Jorati, Department of Mathematics, UBC Subject:Singular kernels adapted to curved flags'' Location: West Mall Annex, Room 110 Abstract: The classical theory of Calderon-Zugmund kernels in \mathbb{R}^n exploits the study of distributions that are almost invariant under the class of isotropic dilations. In this talk we consider convolution operators with distributions that behave simply under a specified class of nonisotropic dilations in the plane. The prototypical example being the operator of Hilbert transform along the parabola in \mathbb{R}^2. Using machinery of flag kernels and multipliers, developed by Nagel, Ricci, Stein, we describe the form of the multiplier for such operators, and, as a corollary, prove their L^p boundedness for 1 Time and Date: 3:30--4:20 p.m., Tuesday, September 27, 2005 Event: Joint SFU/UBC Discrete Math Seminar at SFU Speaker: Richard Anstee, UBC Subject:Forbidden Configurations: An update'' Location: SFU Campus, Applied Science Building 10908 (IRMACS Seminar Room) Abstract: Forbidden configurations are a kind of forbidden induced 'pattern' in matrices (for those who attended Gabor Tardos' lecture). We say a (0,1)-matrix is simple if it has no repeated columns. Let F be a k x l (0,1)-matrix. We say that a simple matrix A has no F-configuration if no submatrix of A is a row and column permutation of F. We are interested in the extremal function forb(m,F) which is the maximum number of columns in an m-rowed simple matrix that has no F-configuration. A conjecture of Sali and A. predicts the assymptotic behaviour of forb(m,F) for fixed F as m tends to infinity. With Keevash, we develop a stability result for k-uniform t-intersecting set systems that determines forb(m,F) for F being k x 2. With Fleming, Furedi and Sali, we have a linear algebra argument for all but one' k x l F where forb(m,F) is O(m^{k-1}). This is joint work with Peter Keevash, Balin Fleming, Zoltan Furedi, and Attila Sali. Time and Date: 2:00 p.m., Wednesday, September 28, 2005 Event: Mathematical Biology Seminar Speaker: Rodrigo A. Restrepo (Emeritus), Department of Mathematics, UBC Subject:A Plausible Ancestry for the tRNAs'' Location: West Mall Annex, Room 216 (PIMS) Abstract: After examining the frequent occurrences of some RNA segments in 657 prokaryotic gene sequences, this work suggests that the development of the tRNAs began with two small RNA segments, specified here, formed in abundant numbers early in the history of the Earth. These segments may have grown larger and diversified in the manner suggested here, becoming able to interact with some specific amino acids before the emergence of the genetic code. These suggestions are supported here by many statistical tests on the tRNAs of prokaryotes. Time and Date: 2:45--3:35 p.m., Wednesday, September 28, 2005 Event: PIMS Tea Location:West Mall Annex, Room 101 (PIMS Library) Time and Date: 3:30--4:30 p.m., Wednesday, September 28, 2005 Event: Probability Seminar Speaker: Nathanael Berestycki, Department of Mathematics, UBC Subject:Of mice and men (and random walks)'' Location: West Mall Annex, Room 216 Abstract: We study of genome rearrangements, which have the following flavor: given two species (say, mice and men), can we estimate their divergence time, i.e. the time elapsed since their most recent common ancestor? On a mathematical level, this leads to study a striking phase transition for the behavior of the distance of a certain random walk on the symmetric group called the random transposition random walk. Crucially, this problem involves a connection with Erdos-Renyi random graphs and may be formulated in terms of coalescence and fragmentation. Motivated by related biological questions we also study the limiting behavior for the distance of other random walks and try to identify those for which there is a similar phase transition. These examples include random adjacent transpositions, random p-cycles, and a random walk on a random 3-regular graph. Time and Date: 4:00 p.m., Wednesday, September 28, 2005 (refreshments start at 3:30 p.m.) Event: IAM Student-Faculty Seminar Speaker: Alexei Cheviakov, Postdoctoral Fellow, Department of Mathematics, UBC Subject:Modelling the Equilibrium States of Plasmas: PDE Properties, Exact Solutions and Physical Models" Location: LSK 301 (refreshments in LSK 306) Abstract: I will start with a review of some physical phenomena and applications involving plasmas, and present the corresponding model PDEs. We will concentrate on the continuum isotropic model of plasmas -- the system of Magnetohydrodynamics (MHD) equations. It is a fully nonlinear 3D system. Its equilibrium version is known for its very special solution topology. I will discuss necessary physical properties of equilibrium solutions, overview the known methods of construction of exact solutions, and present several families of exact solutions with relevant physical models. One of possible ways of construction of new exact solutions to a PDE system is symmetries -- maps of the solution manifold into itself. I will show how the rich symmetry structure of equilibrium MHD equations significantly extends and diversifies the set of known exact solutions (and corresponding physical models). Differences, similarities and relations of MHD with Navier-Stokes and Euler models will be outlined. Time and Date: 12:30 p.m., Thursday, September 29, 2005 Event: Mathematics Colloquium Speaker: Jeong-Yup Lee, Department of Mathematics, University of Victoria Subject: Pure point diffractive, coincidence,and cut-and-project set in substitution point sets (tilings)'' Location: MATH 203 Time and Date: 3:00--3:50 p.m., Thursday, September 29, 2005 Event: SFU/UBC Number Theory Seminar Speaker: Chris Sinclair, PIMS, SFU, UBC Subject:Counting reciprocal polynomials with integer coefficients'' Location: West Mall Annex, Room 110 Abstract: I'll introduce a method which will allow us to produce asymptotic estimates for the number of reciprocal polynomials with integer coefficients, bounded degree and bounded Mahler measure. This method can be extended to other multiplicative measures of complexity of polynomials. Time permitting, I will demonstrate a connection between these topics and physics. Time and Date: 4:00--5:00 p.m., Thursday, September 29, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker: Robert Elliot, Haskayne School of Business, University of Calgary Subject:Indifference Pricing and Real Options'' Location: West Mall Annex, Room 216 Abstract: The field of real options is based on the simple observation that in many projects, or contracts, there are implicit options. Most of the work on pricing such options is very suspect and often is nothing more than an application of techniques from equity pricing. However, the underlying assets in real options are usually not tradeable which invalidates many of the results. In a paper to appear in a Princeton University Press volume, edited by Rene Carmona, Elliott and van der Hoek have developed a theory of indifference pricing for non tradeable assets which bridges the risk neutral pricing of complete markets and certainty equivalence as used by actuaries. The talk will outline these ideas and show how they can be applied to pricing real options. Time and Date: 4:00--5:30 p.m., Thursday, September 29, 2005 Event: Complex Fluids Seminar Speaker: Boris Stoeber, Department of Mechanical Engineering, UBC Subject:Visco-thermal instabilities in microchannels and a novel micromixing concept based on thermally responsive polymer solutions'' Location: MATH 225 Abstract: Microfluidics, the fluid dynamics on a very small length scale, is a rapidly growing field being driven by new technological applications in the life sciences, materials and chemical sciences. Biotechnology for example has a demand for high-throughput low-cost bioanalysis and synthesis systems for diagnostics and research purposes. Because of the typically small length scales of microfluidic components, the effects driving and dominating fluid motion in microfluidic systems are substantially different from effects in large-scale systems. This requires the development of new flow control strategies for the management of very small liquid volumes. In a novel microflow control strategy poloxamers, heat sensitive polymers, are introduced into the fluid samples. These polymer solutions gel reversibly at elevated temperatures. At ambient temperatures close to the phase transition viscous heating within the fluid can lead to flow unsteadiness. It can cause gel formation along the channel walls either in a periodic manner or until the entire channel is pinched off. When the solution temperature of pressure driven flow is slightly higher than the gel temperature, the Pluronic solution will behave as a highly viscous non-Newtonian liquid. Flow velocity fluctuations develop at increased temperatures. In this flow regime flow instabilities might result from the competing mechanisms of shear-thinning and thermo-thickening of the solution. Rapid heating of these polymer solutions from below the gel temperature to far above results in fast gelation of the material. This effect can be used to build a fast microfluidic valve with integrated electric heaters in a microchannel because heat transfer occurs rapidly across the small channel dimension. Local heating of the fluid results in gel formation and subsequent channel blockage within less than 33 ms. A novel laminar mixing concept employs such active valves that are placed in specific locations in a microchannel system. Cyclic actuation of these valves results in periodic flow redirection in the channel system leading to substantial stretching and folding of the fluid layers. Mixing occurs rapidly and effectively through diffusion across the resulting thin layers. Time and Date: 4:10--5:00 p.m., Thursday, September 29, 2005 Event: SFU/UBC Number Theory Seminar Speaker: Michael Bennett, UBC Subject:Integer points on congruent number curves'' Location: West Mall Annex, Room 110 Abstract: An integer N is called a congruent number if there exists a right-angled triangle with area N, all three of whose sides have rational lengths. Equivalently, N is a congruent number if the elliptic curve y^2 = x^3 - N^2*x has positive Mordell-Weil rank over the rational numbers. In this talk, we consider the question of finding integer points on these elliptic curves and discuss a number of related issues. Time and Date: 3:00 p.m., Friday, September 30, 2005 Event: Mathematics Colloquium Speaker: Vlada Limic, Department of Mathematics, UBC Subject: Lambda-coalescent processes and genealogies'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 4:00 p.m., Friday, September 30, 2005 Event: Specialized Seminar Speaker: Jeong-Yup Lee, Department of Mathematics, University of Victoria Subject: Pure point diffractive substitution point sets are Meyer sets'' Location: MATH 103 Abstract: We say that a point set is a Meyer set if the point set is relatively dense (there is no arbitrary big hole in the space without a point of the point set) and the set of all translations in the point set is uniformly discrete (has minimum separation between elements). The importance of Meyer sets in the theory of long-range aperiodic order has been revealed in many investigations. We show that a substitution point set, which is pure point diffractive, is a Meyer set, and observe that any Meyer substitution point set with an expansion map has a property that eigenvalues of the expansion map form a Pisot family, that is to say, the set of eigenvalues of the expansion map consists of all conjugates of eigenvalues of the map whose modulus larger than or equal to 1. Time and Date: 3:00--4:00 p.m., Monday, October 3, 2005 Event: IAM 2005-2006 Seminar Series Speaker: J.F. Williams, Assistant Professor, Department of Mathematics, SFU Subject:Adaptive Strategies for the Numerical Simulation of PDEs with Finite-Time Singularities'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Many mathematical models of real world phenomena take the form of partial differential equations which may exhibit singularities in finite time. In this talk, I shall discuss adaptive strategies in both space and time for the resolution of such behaviour. This adaptive approach is based on scaling properties of the PDE, which leads to uniform error estimates, rather than on information about particular solutions. Examples in one and two dimensions from a variety of applications will be presented. This is joint work with C. J. Budd (University of Bath). Time and Date: 3:00--4:00 p.m., Monday, October 3, 2005 Event: Algebraic Geometry Seminar Speaker: Michael Thaddeus, Columbia U., PIMS Subject:Stable maps to loop groups, II'' Location: WMAX Room 110 (PIMS) Time and Date: 4:00 p.m., Monday, October 3, 2005 Event: Mathematics Colloquium Speaker: Julia Gordon, Department of Mathematics, University of Toronto Subject: Motivic measure and p-adic groups'' Location: MATH 104 Note: The Mathematics Tea will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 2:00 p.m., Tuesday, October 4, 2005 Event: Algebraic Geometry Seminar Speaker:Julia Gordon, University of Toronto Subject:Are characters of p-adic groups computable?'' Location: WMAX Room 110 Abstract: It is known that in general, it is impossible to have a formula for characters of representations of p-adic groups, because there are examples of the character values that depend on a number of points of elliptic or hyperelliptic curves over finite fields. However, one can ask if the equations for varieties that are responsible for character values can be found explicitly (and if such varieties exist in general). This talk will address these questions (under certain circumstances both answers are positive). We will use the group SL(2, Q_p) as a source of explicit examples for "motivic" calculations. Time and Date: 3:30 p.m., Tuesday, October 4, 2005 Event: DG-MP-PDE Seminar Speaker: Pierpaolo Esposito, Department of Mathematics, UBC Subject:A singularly perturbed Neumann/Dirichlet problem: pointwise concentration towards spike-layer solutions'' Location: WMAX Room 110 Abstract: Keller-Segel and Gierer-Meinhardt proposed a mathematical model to describe the evolution of two substances interacting with different diffusion rates. It leads to a system of two coupled nonlinear parabolic equations. The study of stationary solutions for this problem can be reduced, under some assumption on the diffusion rates, to the study of a singularly perturbed Neumann equation with polynomial nonlinearity. We will give an overview of known results concerning this equation and present some new result in order to outline the strong differences between the case of subcritical and critical nonlinearity, between the concentration phenomena on finitely many points and on higher-dimensional sets. We will also discuss this equation under Dirichlet boundary condition. Time and Date: 3:30--4:30 p.m., Tuesday, October 4, 2005 Event: Discrete Math Seminar Speaker: Laura Dunwoody, UBC Subject:Problems of forbidden configurations'' Location: WMAX Room 216 (PIMS) Time and Date: 2:00 p.m., Wednesday, October 5, 2005 Event: Mathematical Biology Seminar Speaker: Eric Cytrynbaum, Department of Mathematics, UBC Subject:Finding the center - how to solve simple geometry problems at the cellular scale'' Location: WMAX Room 216 Abstract: Fragments of fish melanophore cells can form and center aggregates of pigment granules by dynein-motor-driven transport along a self-organized radial array of microtubules (MTs). I will present a quantitative model that describes pigment aggregation and MT-aster self-organization and the subsequent centering of both structures. The model is based on the observations that MTs are immobile and treadmill, while dynein-motor-covered granules have the ability to nucleate MTs. From assumptions based on experimental observations, I'll derive partial integro-differential equations describing the coupled granule-MT interaction. Scaling arguments and perturbation theory allow for analysis in two limiting cases. This analysis explains the mechanism of aster self- organization as a positive feedback loop between motor aggregation at the MT minus ends and MT nucleation by motors. Furthermore, the centering mechanism is explained as a global geometric bias in the cell established by self-nucleated microtubules. Numerical simulations lend additional supports to the analysis. The model sheds light on role of polymer dynamics and polymer-motor interactions in cytoskeletal organization. Time and Date:2:45--3.35 p.m., Wednesday, October 5, 2005 Event: PIMS Tea Location:WMAX Room 101 (PIMS Library) Time and Date: 3:30 p.m., Wednesday, October 5, 2005 Event: Algebra Topology Seminar Speaker: Steve Smith, University of Illinois at Chicago Subject:Homotopy decompositions and classifying spaces for sporadic simple groups'' Location: WMAX Room 110 Abstract: In the case of simple groups, it can be advantageous to seek a decomposition with further properties not necessarily possessed by the usual decomposition---for example, one with minimum possible dimension for computational purposes. A long-term project with Dave Benson has achieved this goal for the 26 sporadic simple groups. The talk will indicate some of the history and background; leading up to some of the intriguing similarities in the behavior of these very different groups. Time and Date: 3:30--4:30 p.m., Wednesday, October 5, 2005 Event: Probability Seminar Speaker: David Brydges, Department of Mathematics, UBC Subject:Joint density for the local times of continuous-time random walks'' Location: WMAX Room 216 Abstract: We investigate the local times of continuous-time random walks on arbitrary discrete state spaces. For fixed finite range of the random walk, we derive an explicit formula for the joint density of all local times on the range, at any fixed time. We apply this formula in the following directions (1) We prove the analog of the well-known Ray-Knight description of Brownian local times for continuous-time simple random walk on \Z, (2) we derive large deviation estimates for exponential integrals of the normalized local times beyond the exponential scale. Time and Date: 4:00 p.m., Wednesday, October 5, 2005 Event: IAM Student-Faculty Seminar Speaker: Nataliya Ivanova, Department of Mathematics, UBC Subject:Symmetries of Differential Equations'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: In this lecture we will give a notion of symmetry (invariance) transformation of differential equations and consider different types of symmetries. A constructive algorithmic way of finding Lie symmetries will be presented. We will consider several applications of symmetries to solving differential equations. Time and Date: 4:00--5:00 p.m., Thursday, October 6, 2005 Event: Graduate Student Seminar Speaker: Warren Code, Department of Mathematics, UBC Subject:Sturm-Liouville problems with boundary conditions that depend on the eigenparameter'' Location: MATX 1102 Time and Date: 4:00--5:30 p.m., Thursday, October 6, 2005 Event: Complex Fluids Seminar Speaker: Speaker: Chunfeng Zhou, Department of Chemical & Biological Engineering, UBC Authors: Chunfeng Zhou, Pengtao Yue and James J. Feng Subject:A computational study of drop formation in microfluidic devices'' Location: MATH 225 Abstract: Capillarity has a prominent role in flow in microfluidic devices because of the typically small linear dimensions, large curvature and large surface area in these geometries. Applications of micro-drops and micro-bubbles in small channels range from micro-pumps to ultrasound contrast agents [1]. In this study, we concentrate on the process of drop formation in microdevices, which has been used for generating uniform emulsions of Newtonian and non-Newtonian fluids, with an emphasis on the effects of fluid rheology. The bulk rheology and interfacial motion are described in a phase-field framework [2], and the numerical solution uses a finite-element algorithm with adpative meshing to ensure proper resolution of the interfaces. We will present simulations of drop formation at the tip of a jet inside a flow-focusing device as demonstrated in recent experiments [1,3]. The rheology of the components may be Newtonian, viscoelastic with the Oldroyd-B models being used for the latter. Results show that component rheology is a major determinant in the morphology of the jet, the details of the breakup process, and the size distribution of drops. The solutions compare favorably with experiments. Time and Date: 3:00 p.m., Friday, October 7, 2005 Event: Mathematics Colloquium Speaker: Steve Smith, University of Illinois at Chicago Subject: Quasithin groups and the classification of the finite simple groups'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 12:30 p.m., Tuesday, October 11, 2005 Event: SCAIM Seminar Speaker: Challa S. Sastry, Department of Earth and Ocean Sciences, UBC Subject:Multiresolution Methods and Applications'' Location: CS X736 (7th floor of the new CS Bldg.) PLEASE NOTE THIS LOCATION. Abstract: The multiresolution algorithms, provided by the wavelets, enable us to divide a complicated function into several simpler ones and study them separately. This property along with their localization property makes them very attractive in the implementations of analysis and synthesis problems that arise in different real life applications. The presentation aims at discussing the multiresolution algorithms along with some of their applications to information retrieval from image databases, image reconstruction in tomography etc. Time and Date: 3:30--4:30 p.m., Tuesday, October 11, 2005 Event: SFU/UBC Discrete Mathematics Seminar Speaker: Bojan Mohar, SFU Subject:Quadrangulations, Eulerian triangulations and 5-critical graphs'' Location: SFU, IRMACS Centre, ASB 10900 (www.irmacs.ca) Abstract: Quadrangulations of the projective plane (and of other nonorientable surfaces) have interesting properties in relation to graph colorings. Some of them will be uncovered in this talk and applied to the study of colorings of locally 3-colorable triangulations. Time and Date: 3:30 p.m., Tuesday, October 11, 2005 Event: DG-MP-PDE Seminar Speaker: Zhiqin Lu, UC Irvine Subject:Weil-Petersson geometry on Calabi-Yau moduli'' Location: WMAX 110 (PIMS Seminar Room) Abstract: In this talk, we study the differential geometry of the CY moduli. We prove the following results on the CY moduli: first, the integrations of the Chern classes of the Weil-Petersson metric are rational numbers, second, we give a condition on the incompleness of the Weil-Petersson metric when the dimension of the moduli space is greater than 1. This work is joint with Michael Douglas and Eisuke Natsukawa. Time and Date: 4:30 p.m., Tuesday, October 11, 2005 Event: DG-MP-PDE Seminar Speaker: Massimiliano Berti, Department of Mathematics & Statistics, McMaster University Subject:Nonlinear oscillations in Hamiltonian PDEs'' Location: WMAX 110 (PIMS) Abstract: The classical problem of finding periodic and quasi-periodic solutions of nonlinear Hamiltonian PDEs has substantially progressed by a new interplay between variational methods, dynamical systems techniques and Nash-Moser implicit function theorems. We present new recent existence results for both free and forced vibration problems in nonlinear wave equations, where both infinite dimensional bifurcation problems and small divisors difficulties arise. Time and Date: 2:00 p.m., Wednesday, October 12, 2005 Event: Mathematical Biology Seminar Speaker: Nicola Fameli, Department of Physics & Astronomy, UBC Subject:Modeling of Ca2+ transport in smooth muscle cells'' Location: WMAX 216 (PIMS) Abstract: I will present a stochastic numerical model simulating the transport of calcium ions (Ca 2+) within the junctional spaces between the plasma membrane and the sarcoplasmic reticulum of smooth muscle cells. In this type of cells, release of Ca 2+ from the sarcoplasmic reticulum (SR) is thought to be responsible for contractile activation. In this scenario, measurements of [Ca 2+] oscillations suggest that to replenish the sarcoplasmic reticulum and maintain contraction, Ca 2+ from the extracellular space are taken up by the sarcoplasmic reticulum having traversed the buffer spaces between the plasma membrane (PM) and the SR. These spaces are known as junctions. The model assumes the propagation of Ca 2+ occurs by diffusion through the junctional cytosol between the PM and the SR. The typical path of Ca 2+ diffusing inside the junctional space is therefore simulated as a three- dimensional random walk from ion sources to ion sinks, representing the ion transporters Na +/Ca2+ exchanger and SERCA pumps, respectively. Results of this study in conjunction with [Ca 2+], force transduction and electron microscopy measurements seem to reinforce the idea that Ca 2+ uptake via PM-SR junctions is a possible and plausible pathway to refilling SR calcium to maintain contractions in smooth muscle cells. Time and Date: 2:45--3.35 p.m., Wednesday, October 12, 2005 Event: PIMS Tea Location: WMAX Room 101 (PIMS Library) Time and Date: 3:30 p.m., Wednesday, October 12, 2005 Event: Algebra Topology Seminar Speaker: Marston Condor, University of Auckland Subject:Group actions on hyperbolic 3-manifolds'' Location: WMAX Room 110 Abstract: Recently it was proved by Gehring, Marshall and Martin (but not yet published) that the discrete subgroup of Iso(H^3) of smallest co-volume is the normaliser Gamma of the [3,5,3]-Coxeter group. Hence the hyperbolic 3-manifolds with maximal symmetry group are those of the form M = H^3/K where K is a torsion-free normal subgroup of Gamma. (This makes Gamma the 3-dimensional analogue of the (2,3,7) triangle group in terms of its role in the Hurwitz bound |{m Aut}(S)| le 84(g-1) for a compact Riemann surfaces of given genus g > 1.) In this talk I will describe methods for finding torsion-free subgroups in Gamma, and constructions showing that infinitely many linear fractional groups PSL(2,q) and PGL(2,q) and all but finitely many alternating groups A_n and symmetric groups S_n are homomorphic images of Gamma and/or its orientation-preserving subgroup Gamma^{+}. As a consequence of this construction, we have an alternative proof of Kojima's theorem that every finite group acts fixed-point-freely on some hyperbolic 3-manifold. This is joint work with Anna Torstensson (Lund) and Gaven Martin (Auckland). Time and Date: 3:30--4:30 p.m., Wednesday, October 12, 2005 Event: Probability Seminar Speaker: Chris Hoffman, U Washington Subject:Coexistence for Richardson type competing spatial growth models'' Location: WMAX Room 216 Abstract: In the Richardson growth model the vertices in Z^d can take on three possible states 0,1, and 2. Vertices in states 1 and 2 remain in their states forever, while vertices in state 0 which are adjacent to a vertex in state 1 (or state 2) can switch to state 1 (or state 2). We think of the vertices in states 1 and 2 as infected with one of two infections while the vertices in state 0 are considered uninfected. We start the models with a single vertex in state 1 and a single vertex is in state 2. We show that with positive probability state 1 reaches an infinite number of vertices and state 2 also reaches an infinite number of vertices. The key tool is applying the ergodic theorem to stationary first passage percolation. Time and Date: 4:00 p.m., Wednesday, October 12, 2005 Event: IAM Student-Faculty Seminar Speaker: Bo Wahlberg, Department of Signal, Sensors & Systems, Royal Institute of Technology, Stockholm, Sweden Subject:Modelling and Identification with Rational Orthogonal Basis Functions'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Models of dynamical systems are of great importance in almost all fields of science and engineering, and in particular in control and signal processing. System identification deals with the problem of estimating and validating such models from experimental data. By approximating the frequency response of a linear time-invariant system by a finite sum of exponentials, the problem of modeling and identification is considerably simplified. This corresponds to finite impulse response models in the time domain. However, by using instead infinite impulse response transfer functions as basis functions, much more efficient model structures can be obtain. Over the last decades a general theory has been developed which generalizes the work on Laguerre functions by Wiener in the 1930s, for the construction and analysis of general rational orthogonal basis functions models for the class of stable systems. The purpose of this presentation is to give an introduction and to discuss some recent applications in system identification of this theory. We will, in particular, discuss how to use orthogonal state-space realization theory and a certain transformation analysis to derive and analyze such models. The theory of rational orthogonal functions is closely related to certain reproducing kernel spaces. This connection can be used to analyze certain problems in system identification, and we will present some recent results in the input design based on these results. Time and Date: 3:00--3:50 p.m., Thursday, October 13, 2005 Event: SFU/UBC Number Theory Seminar at SFU Speaker: Vishwa Dumir, Panjab University Subject:View-obstruction problems'' Location: SFU Campus, Room ASB 10900 Abstract: We present a survey of the topic of view-obstruction problems (generalizations of the problem of which lattice points are visible from the origin) that will be accessible and interesting to graduate students and researchers alike. Time and Date: 4:00--5:00 p.m., Thursday, October 13, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker: Traian Pirvu, Department of Mathematics, UBC Subject:Satisfying Convex Risk Limits by Trading'' Location: WMAX Room 216 Abstract: We take as given a finite set of valuation and stress measures, which we call scenario measures. With each scenario measure there is an associated floor. These measures and floors determine if a random variable, representing the wealth of an agent at the final time, is acceptable. The central result of our paper is the characterization of random variables, representing the wealth of an agent at a time prior to the final time, from which the agent can trade to final acceptability. The representation is surprisingly simple and shows, in particular, that if one cannot form a martingale measure as a convex combination of scenario measures, then the final acceptability condition imposes no constraint on the initial wealth. Furthermore we define buyer's and seller's prices for contingent claims. These are like utility indifference prices, except they are based on a concept of risk-measure indifference. The buyer's and seller's prices thus obtained are within the interval of super-replication and sub-replication prices, and in the case of a complete market, coincide with the expected. Time and Date: 4:00--5:30 p.m., Thursday, October 13, 2005 Event: Complex Fluids Seminar Speaker: Pengtao Yue, Department of Mathematics, UBC Subject:A finite-element phase-field method for simulating interfacial dynamics in complex fluids'' Location: MATH 225 Abstract: We present a novel and efficient finite-element method for treating interfacial problems involving rheologically complex fluids. Two key ingredients of the method are a phase-field representation of the interface and an adaptive meshing scheme that allows fine interfacial resolution at manageable computational cost. In the phase-field framework, the interface is seen as a thin layer across which material properties change rapidly but continuously. Thus, a set of governing equations are derived that hold for both fluids across the interface. This circumvents the cumbersome task of interface tracking. The surface tension emerges from the mixing energy at the interface, and the energy-based formalism easily incorporates complex rheology. The challenge of the method lies in resolving the interfacial layer on a fixed Eulerian grid. This is handled by adaptive meshing on a unstructured grid using the phase-field as the criterion for local refinement and coarsening. We will present several simulations on drop deformation, retraction, coalescence and breakup for Newtonian and viscoelastic liquids and nematic liquid crystals. While some of these serve as validations of our new method, the results also reveal novel physics governing the interplay between interfacial dynamics and bulk rheology. Time and Date: 4:10--5:00 p.m., Thursday, October 13, 2005 Event: SFU/UBC Number Theory Seminar Speaker: Jason Bell, SFU Subject:A generalized Skolem-Mahler-Lech theorem for affine varieties'' Location: SFU Campus, Room ASB 10900 Abstract: The Skolem-Mahler-Lech theorem says that if f(n) is a linear recurrence over a field of characteristic 0, then the set of n such that f(n)=0 is a finite union of arithmetic progressions possibly augmented by a finite set. In this talk, we prove the following generalization of this result: Let X be an affine variety over a field of characteristic 0 with an automorphism s and subvariety Y. If x is a point in X, then the set of integers n such that sn(x) ? Y is a finite union of two-way arithmetic progressions possibly augmented by a finite set. We discuss how this is a generalization of the classical Skolem-Mahler-Lech theorem and discuss recent progress in obtaining a positive characteristic analogue of this result. Time and Date: 3:00 p.m., Friday, October 14, 2005 Event: Mathematics Colloquium Speaker: Jim Bryan, UBC Subject: Topological Quantum Field Theory and its applications ancient and modern'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, October 17, 2005 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: Eitan Tadmor, Department of Mathematics, Institute for Physical Science & Technology, Director of the Center for Scientific Computation and Mathematical Modeling, University of Maryland Subject:Edge Detection, Hierarchical Decompositions and Velocity Averaging'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: I will discuss three separate problems which are dominated by the presence of different scales. The first problem deals with edge detection in noisy spectral data using separation of scales. The second problem originates with image processing: I will present a novel representation of texture which is decomposed into hierarchical scales of edges. I will conclude with velocity averaging of kinetic to macroscopic scales, deriving new regularizing effects in nonlinear second-order equations. Time and Date: 3:00--4:00 p.m., Monday, October 17, 2005 Event: Algebraic Geometry Seminar Speaker: Naichung Conan Leung, CUHK, Hong Kong Subject:Mirror symmetry and magic square'' Location: WMAX Room 110 (PIMS) Time and Date: 3:45 p.m., Monday, October 17, 2005 Event: Mathematics Tea Location: MATX 1115, (Math Lounge) Note: These refreshments precede the 4:00 p.m. Math Colloquium. Time and Date: 4:00 p.m., Monday, October 17, 2005 Event: Mathematics Colloquium Speaker: Michael Cowling, University of New South Wales Subject: Mappings that preserve families of curves'' Location: MATH 104 Time and Date: 12:30--2:00 p.m., Tuesday, October 18, 2005 Event: SCAIM Seminar Speaker: Ching-Shan Chou, Division of Applied Mathematics, Brown University Subject:High order residual distribution finite difference WENO schemes for steady state conservation laws on non-smooth meshes'' Location: MATX 1118 Abstract: High order conservative finite volume and finite difference methods are widely used in solving hyperbolic conservation laws. Finite difference schemes are preferred due to the smaller computational cost for multi-dimensional problems. However, the restriction for using finite difference schemes is the smoothness of the meshes. In this talk, I will first compare these two schemes, and then introduce another type of scheme, "Residual Distribution (RD) Schemes". Starting from RD schemes, we are able to design high order RD finite difference WENO schemes for steady state conservation laws. Our schemes have the cost comparable to finite difference schemes on Cartesian or curvilinear meshes, but without any smoothness assumptions of the meshes. Numerical results will be given. The ongoing work for schemes generalized to convection-diffusion equations and preliminary numerical results will also be presented. Time and Date: 3:30--4:30 p.m., Tuesday, October 18, 2005 Event: Discrete Mathematics Seminar Speaker: Kristin Parton, Department of Mathematics, UBC Subject:Bounds on the Achromatic Number of Triple Systems'' Location: WMAX 216 (PIMS) Abstract: A complete k-colouring of a hypergraph is an assignment of k colours to the points such that (1) there is no monochromatic hyperedge, and (2) identifying any two colours produces a monochromatic hyperedge. The achromatic number of a hypergraph is the maximum k such that it admits a complete k-colouring. This talk will present the maximum possible achromatic number among all maximal partial triple systems and give bounds on the maximum and minimum achromatic numbers of Steiner triple systems. Time and Date: 3:30 p.m., Tuesday, October 18, 2005 Event: DG-MP-PDE Seminar Speaker: Hideo Takaoka, Kobe and Chicago Subject:Global wellposedness for the modified Benjamin-Ono equation in the energy space'' Location: WMAX 110 (PIMS) Abstract: I will prove global existence of a solution for the cubic Benjamin-Ono equation in the energy space. I will also discuss some illposedness issues. This is joint work with Carlos Kenig. Time and Date: 4:00 p.m., Tuesday, October 18, 2005 Event: Representation Theory Seminar Speaker: Jose Antonio de la Pe~na, National University of Mexico Subject:Stable representations of quivers'' Location: MATH 203 Abstract: Objects that are stable for a certain slope were considered in algebraic geometry for a long time. In particular stable vector bundles and stable sheaves play an important role. Let Q be a finite quiver without oriented cycles and k an algebraically closed field. We investigate stable finite dimensional representations of Q. This includes, Harder-Narasimhan filtrations and wall systems. We consider distinguished slopes which preserve the structure of the category of indecomposable representations of Q. Time and Date: 4:30 p.m., Tuesday, October 18, 2005 Event: DG-MP-PDE Seminar Speaker: Yiming Long, Nankai University, China Subject:Closed geodesics on 2 dimensional spheres'' Location: WMAX 110 Abstract: The study of closed geodesics on spheres is a classical and important problem in both dynamical systems and differential geometry. The results of V. Bangert in 1993 and J. Franks in 1992 prove that for every Riemannian metric on S^2 there exist infinitely many geometrically distinct closed geodesics. In 1973, A. Katok constructed a remarkable irreversible Finsler metric on S^2 which possesses precisely two distinct prime closed geodesics. Based on this result, D.V. Anosov in his ICM report of 1974 proposed a question: "For the n-dimensional sphere S^n, Katok's example gives an irreversible Finsler metric, arbitrarily near to the standard' metric (to the metric of constant curvature) which has 2[n/2] closed geodesics. This number coincides with the lower bound which one naturally expects for irreversible Finsler metrics on S^n and which can be proved for metrics sufficiently near the standard' metric". Here we denote by [a]=max{k\in \Z|k\leq a} for any a\in \R. Recently Victor Bangert and I proved the following theorem which confirmed Anosov's conjecture for all Finsler 2-spheres. Theorem. (V. Bangert and Y. Long) For every Finsler metric F on the 2- sphere S^2, there exist at least two distinct prime closed geodesics. In my lecture, I shall give a survey on this topic, talk about also some other new results on the stability of closed geodesics, and mention some interesting and hard open problems in this field. Time and Date: 2:00 p.m., Wednesday, October 19, 2005 Event: Mathematical Biology Seminar Speaker: Byron Goldstein, Los Alamos National Laboratory Subject:Immunoadhesins and monoclonal antibodies in the treatment of disease: Modeling how they couple target cells to natural killer cells'' Location: WMAX 216 (PIMS) Abstract: Natural killer (NK) cells can destroy cells coated with antibody. The killing occurs at close range and requires that NK cells and target cells adhere. The antibodies mediate adhesion and bridge the two cells by binding to sites on the target cell through their Fab regions and by binding to Fc receptors on the NK cells through their constant region. A number of monoclonal antibodies and antibody like molecules have been developed and approved by the FDA to target over expressed normal proteins on tumor cells and cells that drive autoimmune diseases. We present a physical model of NK cell-target cell adhesion mediated by these drugs. We illustrate the properties of the model and determine important physical parameters by using it to fit quantitative data on adhesion of T cells to NK cells mediated by a drug, Alefacept, used in the treatment of psoriasis, an autoimmune disease of the skin. We discuss quantitative predictions of the model, focusing on how drugs can discriminate among cells expressing the same target molecules but with different surface densities. The model offers an explanation of how Alefacept can distinguish target from normal T cells. Time and Date: 2:45--3:35 p.m., Wednesday, October 19, 2005 Event: PIMS Tea Location: WMAX 101 (PIMS Library) Time and Date: 3:00--4:00 p.m., Wednesday, October 19, 2005 Event: Algebraic Geometry Seminar Speaker: Prakash Belkale, University of North Carolina at Chapel Hill Subject:Intersection theory of homogenous spaces and sections of theta bundles on curves'' Location: MATX 1102 Abstract: Classically the intersection theory of Grasmannians is related to invariant theory of the general linear group. I will talk about the geometrization of this correspondence, and extension to geometrizations of similar relations (Quantum cohomology of Grassmannians and sections of theta bundles over moduli of parabolic bundles which is a theorem of Witten). I will then speculate about the higher genus generalizations of such relations. Time and Date: 3:30--4:30 p.m., Wednesday, October 19, 2005 Event: Probability Seminar Speaker: Gabor Pete, UC Berkeley Subject:Corner percolation and the square root of 17'' Location: WMAX 216 Abstract: We consider a dependent bond percolation model on Z^2, introduced by Balint Toth, in which every edge is present with probability 1/2, and each vertex has exactly two incident edges, perpendicular to each other. We prove that all components are finite cycles almost surely, but the expected diameter of the cycle containing the origin is infinite. Moreover, we derive critical exponents: for the tail probability, \Pr(diameter of the cycle of the origin > n) \approx n^{-\gamma}, and for the expectation, \E(length of a cycle conditioned on having diameter n) \approx n^\delta. We show that \gamma=(5-\sqrt{17})/4=0.219... and \delta=(\sqrt{17}+1)/4=1.28... The relation \gamma+\delta=3/2 corresponds to the fact that the scaling limit of the natural height function in the model is the Additive Brownian Motion, whose level sets have Hausdorff dimension 3/2. The exponent \delta comes from the solution of a singular sixth order ODE. Time and Date: 4:00 p.m., Wednesday, October 19, 2005 Event: IAM Student-Faculty Seminar Speaker: Omer Dushek, Department of Mathematics, UBC Subject:Calculating Diffusion Coefficients for Cell Surface Molecules using the Fluorescence Recovery after Photobleaching (FRAP) Technique'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: A common technique for determining the diffusion coefficient of cell surface molecules is Fluorescence Recovery After Photobleaching (FRAP). In this technique, cell surface molecules are tagged with a fluorochrome so that they can be seen under the microscope. In a certain region of the cell surface, the fluorochromes are denatured, causing the fluorescence in this region to decrease by a large amount (roughly 60 percent). Over time, the fluorescence recovers as receptors diffuse back into this region. A popular equation to fit this data is an approximate solution to the 1-D diffusion equation. I will show that the error in using this equation for the space and time scales of experimental observation is quite large. I will then present an equation more suitable for these scales. Time and Date: 4:00--5:00 p.m., Thursday, October 20, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker: Artyom Shneyerov, Department of Economics, UBC Subject:Dynamic matching, two-sided incomplete information, and participation costs: existence and convergence to perfect competition'' Location: WMAX 216 Abstract: Consider a decentralized, dynamic market with an infinite horizon and participation costs in which both buyers and sellers have private information concerning their values for the indivisible traded good. Time is discrete, each period has length ?, and each unit of time continuums of new buyers and sellers consider entry. Traders whose expected utility is negative choose not to enter. Within a period each buyer is matched anonymously with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, both the seller and winning buyer exit the market with their realized utility. Traders who fail to trade continue in the market to be rematched. We characterize the steady-state equilibria that satisfy a subgame perfection criterion. We show that, as ? converges to zero, equilibrium prices at which trades occur converge to the Walrasian price and the realized allocations converge to the competitive allocation. We also show existence of equilibria for ? sufficiently small. Time and Date: 4:00--5:00 p.m., Thursday, October 20, 2005 Event: Graduate Student Seminar Speaker: Amy Goldlist, Department of Mathematics, UBC Subject:The congruent number problem aka, fun with modular forms'' Location: MATX 1102 Abstract: An ancient Greek problem asks when a number, n, is the area of a right angle triangle with rational sides. If it is, it is called congruent. Via mathematical cunning, the problem of whether n is congruent can be transformed into a question involving elliptic curves. From this step, the jump to modular forms is not a huge stretch of the imagination. I plan on giving an expository talk on the mathematics behind a condition for congruent numbers, and end up with a "complete" answer to the question of whether n is congruent - modulo the Birch-Swinnerton-Dyer conjecture. Time and Date: 4:00--5:00 p.m., Thursday, October 20, 2005 Event: Complex Fluids Lab Grand Opening 1st Speaker: David James, University of Toronto 2nd Speaker: Gareth McKinley, MIT Subject:1st talk: An Introduction to the World of Rheology" Subject:2nd talk: Elasto-capillary thinning and beads-on-a-string" Location: Leonard S. Klinck Bldg. Room 201 Note: The talks will be followed by a reception at 5:00 p.m. in the new lab, LSK 203, all are cordially invited. Time and Date: 3:00 p.m., Friday, October 21, 2005 Event: Mathematics Colloquium Speaker: Prakash Belkale, UNC at Chapel Hill Subject: Eigenvalue problem and a new product in the cohomology of flag varieties'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 2:45 p.m., Monday, October 24, 2005 Event: Mathematics Tea Location: MATX 1115, (Math Lounge) Time and Date: 3:00--4:00 p.m., Monday, October 24, 2005 Event: IAM Seminar Series Speaker: Brian Wetton, UBC Subject:Modeling Hydrogen Fuel Cell Stacks'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: A basic introduction to the idea of a hydrogen energy economy is given, with emphasis on the role of fuel cells. A reduced dimensional model of steady state operation of Polymer Electrolyte Membrane Fuel Cell (PEMFC) stacks with straight gas channels is then presented. The model takes into account many important aspects of fuel cell operation and has been developed to be an aid to fuel cell design in an industrial setting. The structure of the model is a nonstandard system of boundary value Differential Algebraic Equations (DAEs) with strong, nonlocal coupling. A discretization of the system and a succesful iterative strategy is described. Some preliminary analysis of the system and iterative strategy is given, using simple, constant coefficient, linear versions of the key components of the model. Representative computational results are shown. Some interesting mathematical directions suggested by our group's modelling work will be briefly presented. Time and Date: 3:00--4:00 p.m., Monday, October 24, 2005 Event: Algebraic Geometry Seminar Speaker: Jochen Kuttler, Department of Mathematics, UBC Subject:Blowing up certain singularities of T-varieties in G/P'' Location: WMAX Room 110 (PIMS) Abstract: In this talk we study singularities of T-varieties in G/P, where G is a semi-simple algebraic group, P a parabolic subgroup and T a maximal torus. Under good circumstances, isolated singularities are resolved by a one-step blow up. In this case, one has also some control on the fibre of the Nash blow up. The main application of course are Schubert varieties. In parts this is joint work with Jim Carrell. Time and Date: 12:30--2:00 p.m., Tuesday, October 25, 2005 Event: SCAIM Seminar Speaker: Kees van den Doel, Department of Computer Science, UBC Subject:Level set regularization for highly ill-posed distributed parameter estimation problems'' Location: MATX 1118 Abstract: The recovery of a distributed parameter surface with discontinuities from inverse problems with elliptic forward PDEs is fraught with theoretical and practical difficulties. Better results are obtained for problems where the solution may take on at each point only one of two values, thus yielding a shape recovery problem. In this talk, after introducing the subject, I will describe my recent work with Uri Ascher on level set regularization for such problems. Rather than explicitly integrating a time embedded PDE to steady state, which typically requires thousands of iterations, methods based on Gauss-Newton are applied directly. One of these can be viewed as damped Gauss-Newton utilized to approximate the steady state equations which in turn are viewed as the necessary conditions of a Tikhonov type regularization with a sharpening sub-step at each iteration. In practice this method is eclipsed, however, by a special "finite time" trust region (or Levenberg-Marquardt) method which we call dynamic regularization applied to the output least squares formulation. The regularization functional is applied to the (smooth) level set function rather than the discontinuous surface to be recovered, and the second focus of this work is on selecting this functional. Typical choices may lead to (or at least not avoid) flat level sets which in turn cause ill-conditioning in that a small point-wise change in the level set function causes a large change in its 0-level and hence in the recovered surface. But the regularization should also be selected so that its evolution is smooth, a particularly important concern when large iteration updates are contemplated. We propose a new, quartic, non-local regularization term and compare its performance to more usual choices. Two numerical test cases are considered: a potential problem and the classical EIT/DC resistivity problem. Time and Date: 3:30--4:30 p.m., Tuesday, October 25, 2005 Event: Joint SFU/UBC Discrete Math/Computer Science Theory Seminar Speaker: David Kirkpatrick, UBC Subject:Minimizing precision/input in the evaluation of geometric primitives'' Location: WMAX 216 (PIMS) Abstract: Suppose that S is a collection of n points, each specified by k-bit coordinates. We want to determine some property of S: for example, does one distinguished point in S lie in the interior of the convex hull of the rest. For some instances S, all (or most) of the bits of all (or most) of the points need to be examined in order to determine the property; for other instances the property can be established by examining only a (relatively) small number of bits. In general we would like to devise algorithms whose cost (number of bits examined) adapts to the intrinsic cost (shortest "proof" of the property) for a particular input. The problem of constructing such algorithms for certain simple geometric primitives was posed by Leo Guibas. I will describe some preliminary results concerning certain very basic questions of this type, based on joint work with Raimund Seidel. Time and Date: 3:30 p.m., Tuesday, October 25, 2005 Event: DG-MP-PDE Seminar Speaker: Adam Oberman, SFU Subject:Numerical Approximation of first and second order nonlinear elliptic PDEs and stochastic game interpretations'' Location: WMAX 110 (PIMS) Abstract: The theory of viscosity solutions gives powerful existence, uniqueness and stability results for first and second order degenerate elliptic equations. The approximation theory developed by Barles and Sougandis in the early nineties gave conditions for the convergence of numerical schemes. Building on this work, we develop convergent schemes for nonlinear second order equations, including: infinity laplacian, motion by mean curvature, the Monge-Ampere equation, and the equation for the convex hull. Many of these equations also have interpretations as stochastic control problems. We'll discuss this, and briefly give discrete control interpretations of the schemes. Time and Date: 2:00 p.m., Wednesday, October 26, 2005 Event: Mathematical Biology Seminar Speaker: Nima Geffen, Mathematics, Tel Aviv University Subject:A micro helical organism re-visited'' Location: WMAX 216 (PIMS) Abstract: A spiroplasma, a helical prokaryot. is, arguably, the smallest free swimming, autonomous living. It is driven by a linear protein cytoskeleton that controls it's shape and motion. How is this effected? A probable mechanism for a set of basic helical conformations will be reviewed, and related to the rich repertoire of observed forms of the swimming organism. New, possibly conflicting published data will be presented and discussed. Time and Date: 2:45-3:35 p.m., Wednesday, October 26, 2005 Event: PIMS Tea Location: WMAX 101 (PIMS Library) Time and Date: 3:00--4:00 p.m., Wednesday, October 26, 2005 Event: Algebraic Geometry Seminar Speaker: Shahn Majid, Queen Mary, University of London Subject:Noncommutative differential geometry and the origin of time'' Location: MATX 1102 Abstract: Noncommutative geometry is a more general formulation of geometry that does not require coordinates to commute. As such it unifies quantum theory and geometry and should appear in any effective theory of quantum gravity. In this general talk we present quantum groups as a microcosm of this unification in the same way that Lie groups are a microcosm of usual geometry. We use them to construct differential structures on finite groups or finite Lie theory'. We also explain that noncommutative spaces typically carry a canonical 1-parameter evolution or intrinsic time created from the fundamental conflict between noncommuting coordinates and differential calculus.) Time and Date: 3:30--4:30 p.m., Wednesday, October 26, 2005 Event: Probability Seminar Speaker: Vlada Limic, UBC Subject:The spatial Lambda-coalescent'' Location: WMAX 216 Abstract: This talk is based on a joint paper with Anja Sturm, and it will describe the extension of the Lambda-coalescent of Pitman (1999) to the spatial setting. The partition elements of the spatial Lambda-coalescent migrate in a (finite) geographical space and may only coalesce if located at the same site of the space. We characterize the Lambda-coalescents that come down from infinity, in an analogous way to Schweinsberg (2000). Surprisingly, all spatial coalescents that come down from infinity, also come down from infinity in a uniform way. This enables us to study space-time asymptotics of spatial Lambda-coalescents on large tori in transient dimensions. Our results generalize and strengthen those of Greven et al. (2005), who studied the spatial Kingman coalescent in this context. Time and Date: 4:00 p.m., Wednesday, October 26, 2005 Event: IAM Student-Faculty Seminar Speaker: Dan Coombs, UBC Subject:Understanding parasite fitness in simple models'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Viruses compete and are subject to natural selection at multiple levels: within-cell, within-host and within-population (of hosts). We looked at how viruses can optimally exploit their hosts and how this behaviour may influence the most successful strategy at the between-host, or epidemiological level. I'll illustrate this all as best I can and try not to be boring or confusing. Time and Date: 3:00--3:50 p.m., Thursday, October 27, 2005 Event: SFU/UBC Number Theory Seminar at UBC Speaker: Nigel Boston, University of Wisconsin Subject:Galois groups of p-extensions and applications'' Location: UBC Campus, WMAX 110 (PIMS Seminar Room) Abstract: Unlike the ramified-at-p case, Galois groups of p-extensions unramified at p are poorly understood, partly because they should have only finite-image p-adic representations. We present an analogous theory of arboreal representations, a nonabelian Jugendtraum, and nonabelian Cohen-Lenstra heuristics. Applications of this theory to root-discriminant problems, algebraic topology, and group theory have emerged. Time and Date: 4:00--5:00 p.m., Thursday, October 27, 2005 Event: Complex Fluids Seminar Speaker: Teodor Burghelea, Department of Mathematics, UBC Subject:Chaotic flow and mixing with a dilute polymer solution in a regime of elastic turbulence'' Location: MATH 225 Abstract: I present an experimental investigation of random flows of a dilute polymer solution above the onset of the elastic instability in both closed and open flow configurations [1]. Systematic investigation [2,3] of micro flows of a dilute polymer solution has shown that, when elastic stresses overcome the viscous ones (Wi>1), the micro flow becomes quite irregular and evolves (as Wi is further increased) rapidly towards a fully developed chaotic regime. Although the typical size of the elongated polymer molecules is likely to become comparable to the diameter of the micro channel , we show that the random micro flow of a dilute polymer solution surprisingly displays most of the features of elastic turbulence (Groisman and Steinberg, Nature, 2000) in geometrically similar macro flows: \emph{fast growth of flow resistance, randomly varying and strongly fluctuating velocity fields, fast and monotonous decay of the Eulerian velocity correlations}. The random microscopic flow turns out to be an ideal realization of the Batchelor regime of mixing. By studying the mixing efficiency at different Peclet numbers (Pe), we confirm a very recent theoretical prediction (Chertkov and Lebedev, 2003): the mixing efficiency scales algebraically with Pe. This difference with respect to the case of the Batchelor regime in an unbounded system is further clarified by systematic measurements of the width of the mixing boundary layer as a function of Pe. Finally, we characterize the flow randomness in a regime of elastic turbulence by focusing on the statistics of particle pair separations [1,4]. We compare the Finite Time Lyapunov Exponents (FTLE) with the statistical description in Eulerian frame, namely velocity correlation times and average velocity gradients. Time and Date: 4:10--5:00 p.m., Thursday, October 27, 2005 Event: SFU/UBC Number Theory Seminar Speaker: Patrick Ingram, Department of Mathematics, UBC Subject:Primitive divisors in elliptic divisibility sequences'' Location: UBC Campus, WMAX 110 Abstract: A divisibility sequence is a sequence of intregers {an} with the property that an divides am whenever n divides m. We will survey the literature on divisibility sequences and consider various problems relating to elliptic divisibility sequences, a certain class of sequences arising from the study of elliptic curves. In particular, we will ask whether the terms in such a sequence must eventually all have primitive divisors, that is, divisors that divide no previous term in the sequence. Time and Date: 3:00 p.m., Friday, October 28, 2005 Event: Mathematics Colloquium Speaker: Nigel Boston, University of Wisconsin Subject: Invariant-based Face Recognition'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 2:45 p.m., Monday, October 31, 2005 Event: Mathematics Tea Location: MATX 1115, (Math Lounge) Time and Date: 3:00--4:00 p.m., Monday, October 31, 2005 Event: IAM Seminar Series Speaker: Neil Balmforth, Department of Mathematics, UBC Subject:Snailballs and More'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: The "snailball" is a magic trick wherein an apparently solid metal sphere rolls slowly and erratically down an inclined plane. The key to the trick is that the sphere is not actually solid throughout, but a shell containing a second, smaller sphere with a very viscous fluid sandwiched between. As will be demonstrated in the seminar, the same phenomenon occurs when a combination of cylinders rolls down a surface. A mathematical model of the latter is presented to explore in more detail the motions of the two cylinders. A key feature of the predicted dynamics is that the inner cylinder cannot be suspended in the fluid by the rolling motion of the outer cylinder. Instead, it must always fall toward the outer cylinder and "contact". The rocking and rolling motion of the real cylinders must then incorporate a key extra physical detail, namely what happens when the cylinder surfaces become very close. Two possibilities are discussed: contact between rough surface, and cavitation. Time and Date: 3:00--4:00 p.m., Monday, October 31, 2005 Event: Algebraic Geometry Seminar Speaker: Konstanze Rietsch, King's College, University of London Subject:Mirror families for flag varieties G/P and the Peterson variety'' Location: WMAX 110 (PIMS) Abstract: We give a Lie-theoretic construction of a conjectural mirror family in the sense of Givental to a general flag variety G/P, and show that this mirror family recovers the Peterson variety presentation for the quantum cohomology rings qH^*(G/P)_{(q)}. As a nice application one can use this approach to describe the totally nonnegative part of the Peterson variety in type A. Time and Date: 12:30--2:00 p.m., Tuesday, November 1, 2005 Event: UBC SCAIM Seminar Speaker: Ian Mitchell, Department of Computer Science, UBC Subject:Some Algorithms, Software and Applications of Hamilton-Jacobi PDEs'' Location: MATX 1118 Abstract: Hamilton-Jacobi type (HJ) PDEs arise in optimal control, dynamic implicit surfaces for fluid animation and simulation, image processing, and many other fields. There are two broad classes of equations: time-dependent and stationary. Level set methods are a group of finite difference algorithms for the former class of equations, and I will describe a publicly released toolbox of Matlab routines for approximating a wide variety of common HJ forms in any dimension. I will then describe and analyze a new algorithm for solving the stationary form of HJ equations. Finally, I will discuss applications of each of the two forms: reachable sets for the verification of continuous systems, and optimal path planning with multiple objectives. Time and Date: 3:30--4:30 p.m., Tuesday, November 1, 2005 Event: Joint SFU/UBC Discrete Math/Computer Science Theory Seminar Speaker: Jason Bell, Department of Mathematics, SFU Subject:New Methods in the theory of Quasi-invariants'' Location: WMAX 216 (PIMS) Abstract: We introduce a new approach to the study of quasi-invariants. This approach consists of representing quasi-invariants as n-tuples of invariants. Conditions are then sought which characterize such n-tuples. These methods explain certain observed properties of quasi-invariants. This is joint work with A. Garsia and N. Wallach. Time and Date: 3:30 p.m., Tuesday, November 1, 2005 Event: DG-MP-PDE Seminar Speaker: Ivar Ekeland, PIMS, UBC Subject:A remarkable PDE arising from non-commitment in economics'' Location: WMAX 110 (PIMS) Abstract: (joint work with Ali Lazrak and Louis Nirenberg) Optimal control theory has been used to study economic policy. It is not robust, however, to non-commitment by the policy maker. We propose an alternative approach, leading to a remarkable variant of the Hamilton-Jacobi equation. Time and Date: 2:00 p.m., Wednesday, November 2, 2005 Event: Mathematical Biology Seminar Speaker: Nick Swindale, Department of Ophthalmology & Visual Sciences, UBC Subject:Coverage, Polymaps and the Visual Cortex'' Location: WMAX 216 (PIMS) Abstract: In this talk I will present some simple mathematical models that are able to explain the structure of the maps that are found in the mammalian visual cortex. These can be characterized as projections of a 2D surface into a high dimensional feature space subject to completeness and local continuity constraints. Time and Date: 2:45-3:35 p.m., Wednesday, November 2, 2005 Event: PIMS Tea Location: WMAX 101 (PIMS Library) Time and Date: 3:30 p.m., Wednesday, November 2, 2005 Event: Algebra Topology Seminar (This was postponed on Oct. 24, 2005 until Nov. 2nd) Speaker: Denis Sjerve, UBC Subject:Invariant Spin Structures on Hyperelliptic Surfaces'' Location: WMAX 110 Abstract: Atiyah proved that any automorphism of a Riemann surface M of genus at least 2 leaves invariant some spin structure. This raises several questions: how many spin structures are invariant? does the entire automorphism group leave some spin structures invariant? etc. In this talk I will show how to answer the first question for hyperelliptic surfaces. Time and Date: 3:30--4:30 p.m., Wednesday, November 2, 2005 Event: Probability Seminar Speaker: Jean-Francois Delmas, CERMICS, France Subject:Fragmentation of the continuous random tree'' Location: WMAX 216 Abstract: We consider the height process of a Lévy process with no negative jumps, and its associated continuous tree representation. Using Lévy snake tools developed by Duquesne-Le Gall, with an underlying Poisson process, we construct a fragmentation process, which in the stable case corresponds to the self-similar fragmentation described by Miermont. For the general fragmentation process we compute a family of dislocation measures as well as the law of the size of a tagged fragment. Time and Date: 4:00 p.m., Wednesday, November 2, 2005 Event: IAM Student-Faculty Seminar Speaker: Daniel Olmos, Department of Mathematics, UBC Subject:A Numerical Study of Excitable Systems'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Excitable systems are often modelled with reaction-diffusion equations with kinetic terms of varying complexity. The solution of such reaction-diffusion systems is characterized by many different time and length scales. In the present talk, I will discuss the classical Hodgkin-Huxley (HH) model as an example of excitability. After, I will explain the problem of the different time and space scales in systems like the (HH) model, followed by a description of the purpose of my research, which is focused on the numerical simulation of excitable systems. More specifically my research work is directed towards the development of spectral methods for the resolution of the fast and slow dynamics with high accuracy and low computational cost. Time and Date: 4:00--5:00 p.m., Thursday, November 3, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker: Calvin Winter, President, Alpha Lake Financial Analytics Corp. Subject:Mathematical Methods applied to Finance Trading Strategies'' Location: WMAX 216 Abstract: We consider the implications of the arbitrage free condition applied to markets. By considering systematic trading strategies we show that arbitrage free implies: instantaneous adjustment by the market to news; short term volatility is linked to long term volatility by the convolution of the time varying probability distribution functions or as (time)1/2 in the Gaussian case. In the special case of continuous markets then volatility itself becomes tradable and must be arbitrage free, in addition we derive an expression for arbitrage free bid-ask spread which is volatility dependent. Deviations of real market behavior from the arbitrage free case can sometimes provide helpful clues to assist in constructing systematic trading strategies. Time and Date: 4:00--5:00 p.m., Thursday, November 3, 2005 Event: Graduate Student Seminar Speaker: Yinan Song, Department of Mathematics, UBC Subject:Introduction to Lie algebras and their representations'' Location: MATX 1102 Abstract: In this introductory talk, I will define Lie algebra and I will describe a particular infinite dimensional Lie algebra, the Heisenberg algebra. Finally, I will describe how the Heisenberg algebra acts on the homology groups of Hilbert schemes of points on a surface. Time and Date: 4:00--5:00 p.m., Thursday, November 3, 2005 Event: Complex Fluids Seminar Speaker: Laurent Rubatat, Department of Physics, SFU Subject:Probing the micro-structure of carbopol using dynamic light scattering and multiple particle tracking'' Location: MATH 225 Abstract: We study the micro-rheology of dispersions of Carbopol ETD 2050 in water as a function of the gel concentration. To do so, we use dynamic light scattering and optical microscopy to track submicron spherical particles loaded in the gel, with diameter ranging from 50 nm to 1 mm. The Mean Square displacement (MSD) of the particles is calculated and analyzed to obtain the complex mechanical modulus of the gel on micrometer length scales. For low Carbopol concentrations (0.1%), the spheres diffuse. At moderate concentrations (0.5%) there is subdiffusion as the structure of the fluid constrains the sphere motion. At high concentrations (1%), the Carbopol is a stiff gel and the particles are almost completely confined. The results obtained by microscopy and dynamic light scattering are in good agreement. In contrast, we find substantial differences between our micro-scale measurements and the results of lassical shear rheometry. We will discuss the difference between the bulk results and the microscale results in the context of the gel structure. Time and Date: 3:00 p.m., Friday, November 4, 2005 Event: Mathematics Colloquium Speaker: Michael Thaddeus, Columbia University Subject: Holomorphic curves on infinite-dimensional homogeneous spaces'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 2:45 p.m., Monday, November 7, 2005 Event: Mathematics Tea Location: MATX 1115, (Math Lounge) Time and Date: 3:00--4:00 p.m., Monday, November 7, 2005 Event: IAM-PIMS-MITACS 2005-2006 Distinguished Colloquium Series Speaker: Gregory Kriegsmann, Foundation Chair of Applied Mathematics, Professor of Mathematics, Department of Mathematical Sciences, New Jersey Institute of Technology Subject:Microwave Heating of Materials: A Mathematical and Physical Overview'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: The use of microwaves to heat and dry materials is rapidly gaining acceptance in industry and, to some extent, in the field of biomedical engineering. The working engineering theories are based upon heuristically averaged, linear equations which adequately explain some processes, such as microwave cooking of foodstuffs, but not others. These include such phenomenon as thermal runaway and hot-spot formations which have important ramifications in both biomedical and industrial applications. They are caused by the temperature dependencies of the electrical and thermal properties of the irradiated material which make the basic underlying mathematical description highly nonlinear. We shall describe several microwave heating experiments and present models which have been used by researchers in this field. The strengths and shortcomings of these models will be discussed, and open questions of both mathematical and computational natures will be presented. Time and Date: 3:00--4:00 p.m., Monday, November 7, 2005 Event: Algebraic Geometry Seminar Speaker: Yinan Song, Department of Mathematics, UBC Subject:Gromov-Witten/Donaldson-Thomas correspondence'' Location: WMAX 110 (PIMS Seminar Room), 1933 West Mall, UBC Abstract: I will discuss the conjectural correspondence of Gromov-Witten/Donaldson-Thomas theories of threefolds with focus on the theoretical and computational aspects of Donaldson-Thomas theory. I will also discuss some recent results on P^2-bundle over a smooth curve that provide some evidence for this conjecture. Time and Date: 3:30--4:30 p.m., Tuesday, November 8, 2005 Event: Joint SFU/UBC Discrete Math/CS Theory Seminar Speaker: Luis Goddyn, SFU Subject:An Optimization Problem arising from Video-on Demand Broadcasting'' Location: WMAX 216 (PIMS) Abstract: A common protocol (FDPB) for video-on-demand specifies that a large document (a movie) be divided into consecutive time segments s_1, \dots, s_n. The segments are continually broadcast through a single channel according to a specified periodic schedule such as s_1, s_5, s_2, s_1, s_3, s_4, s_1, s_2, s_3, \dots. A client may, at any time, decide to watch the movie. Segments s_i with a small subscript i should appear frequently in the schedule, so the viewer does not have to wait long for the movie to begin. Segments with large i may appear less frequently since they can be loaded while the movie is already playing. An optimal schedule minimizes the initial delay time while guaranteeing that the movie does not have to pause to await a missing segment. A (patented) solution to this problem involves a "round-robin tree". To implement their protocol efficiently, one must solve the following optimization problem. Given a large positive integer n_0, we seek a positive integer d which maximizes n_d, where n_1, n_2, \dots, n_d are defined by n_{i+1} = n_i + \floor( n_i / d ), 0 \le i < d. For a fixed n_0, the value of n_d behaves erratically as a function of d. We show that the optimal value of d can be determined by examining a small interval centred at 1.2578 \sqrt{ n_0 }. This greatly improves the linear-time search proposed by the patent holders (Hollmann et al, 1995). This is joint work with T. Kameda and Y. Sun. Time and Date: 3:30 p.m., Tuesday, November 8, 2005 Event: DG-MP-PDE Seminar Speaker: Nassif Ghoussoub, BIRS, UBC Subject:On the Partial Differential Equations of Electrostatic MEMS Devices'' Location: WMAX 110 (PIMS) Abstract: I will be talking about work with Yujin Guo on the nonlinear parabolic problem u_t=\Delta u -\frac{\lambda f(x)}{(1+u)^2} on a bounded domain \Omega of \R^N with Dirichlet boundary conditions. This models a simple electrostatic Micro-Electromechanical System (MEMS) device consisting of a thin dielectric elastic membrane with boundary supported at 0 above a rigid ground plate located at -1. When a voltage --represented here by \lambda-- is applied, the membrane deflects towards the ground plate and a snap-through may occur when it exceeds a certain critical value \lambda^*. This equation --suggested by Michael Ward-- turned out to be a rich source of interesting mathematical phenomena. Numerics give lots of information and point to many conjectures, and the existing arsenal of nonlinear analysis and PDE techniques can only tackle a precious few. Refined properties of steady states --such as regularity, stability, uniqueness, multiplicity, energy estimates and comparison results-- are shown to depend on the dimension of the ambient space. I will also describe some of the results and questions in the dynamic case: Touchdown or not, in finite or infinite time. Time and Date: 2:00 p.m., Wednesday, November 9, 2005 Event: Mathematical Biology Seminar Speaker: Lin Wang, University of Victoria Subject:Competition in the chemostat'' Location: WMAX 216 (PIMS) Abstract: In this talk, a chemostat model with general nonmonotone response functions is considered. The nutrient conversion process involves time delay. It is shown that under certain conditions, when several species with differential removal rates compete in the chemostat for a single resource that is allowed to be inhibitory at high concentrations, the competitive exclusion principle (CEP) holds. In addition, a local stability analysis is provided that includes sufficient conditions for the bistability of the single species survival equilibrium and the washout equilibrium, thus showing initial condition dependent outcome is possible. This talk is based on joint work with G.S.K. Wolkowicz (McMaster University). Time and Date: 2:45-3:35 p.m., Wednesday, November 9, 2005 Event: PIMS Tea Location: WMAX 101 (PIMS Library) Time and Date: 3:30--4:30 p.m., Wednesday, November 9, 2005 Event: Probability Seminar Speaker: Omer Angel, UBC Subject:One-dimensional DLA'' Location: WMAX 216 Abstract: Diffusion limited aggregation (DLA) in 2 or more dimensions is an infamously difficult model for the growth of a random fractal. DLA was introduced in 1981 and attracted massive attention (63,400 google results for "diffusion limited aggregation"). Kesten's 1987 upper bound is almost the only proven result on it. We define a variation of DLA in one dimension. This becomes interesting when the random walk generating the DLA has arbitrary long jumps. It turns out that the growth rate of the aggregate depends on the step distribution in complex ways. In particular there are three phase transitions in the behaviour when the step distribution has finite expectation, finite variance, and finite third moment. Joint work with Gidi Amir, Itai Benjamini and Gadi Kozma. Time and Date: 4:00 p.m., Wednesday, November 9, 2005 Event: IAM Student-Faculty Seminar Speaker: George Bluman, UBC Subject:Connections between symmetries and conservation laws'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: pdf link: http://www.emis.de/journals/SIGMA/2005/. The classical Noether's Theorem yields conservation laws arising from continuous symmetries of functionals whose extrema solve the corresponding Euler-Lagrange equations. After reviewing Noether's Theorem and its severe limitations, we present the Direct Construction Method to find directly the CLs for any given system of differential equations. The DCM yields the factors for CLs as well as an integral formula for corresponding conserved densities. The factors are symmetries of the given system of DEs if and only if the given system has a variational principle. The action of a symmetry (discrete or continuous) on a conservation law yields conservation laws. Conservation laws of a given system of DEs yield non-locally related systems that, in turn yield algorithms to obtain nonlocal symmetries (and nonlocal conservation laws as well as extensions of qualitative, numerical and perturbation methods) for a given system. Moreover from its admitted symmetries or factors for conservation laws, one can determine whether or not a given system of PDEs can be linearized by an invertible transformation and find its linearization when it exists. All of these connections are algorithmic. Examples will be given and some open problems will be presented. Time and Date: 3:00--3:50 p.m., Thursday, November 10, 2005 Event: SFU/UBC Number Theory Seminar at SFU Speaker: Greg Martin, UBC Subject:Smooth numbers, primes, and Egyptian fractions'' Location: SFU Campus, Room ASB 10900 Abstract: This will be an expository talk about smooth numbers (numbers without large prime factors) and their connection to the distribution of prime numbers, particularly prime values of polynomials. An application to questions on Egyptian fractions (sums of reciprocals of distinct positive integers) will ensue, mainly as an excuse to bring in some of the speaker's old research. The entire talk will be accessible to students and non-experts. Time and Date: 4:00--5:00 p.m., Thursday, November 10, 2005 Event: Complex Fluids Seminar Speaker: Andreas Putz, Department of Mathematics, UBC Subject:Plug breaking and wall-layer formation in a wavy walled channel flow'' Location: MATH 225 Abstract: We show numerical simulation results for the Poiseuille flow of a Bingham fluid down a wavy-walled channel, at long wavelengths. For small amplitude perturbations of the plane channel, the rigid plug region remains intact, but breaks at a critical amplitude. The asymptotic theory in [1] predicts both the shape of the perturbation of the yield surface and the critical amplitude when the plug breaks. Counter-intuitively, the unyielded plug is wider in the narrower part of the channel and narrower in the wider part. Numerically, this is a challenging problem. For high accuracy in a channel of large aspect ratio, a large number of cells are required. Regularisation methods are inappropriate for such geometries and anyway do not necessarily predict the correct yield surface position. We have used finite elements with the augmented Lagrangian method, coupled with an adaptive meshing technique that focuses the mesh close to the yield surface, see [2]. The numerical results confirm the results of [1]. Unequivocally, this means that the lubrication paradox of [3] is in fact no paradox, i.e. it is simply that appropriate numerical and asymptotic methods must be applied. The numerical results are able to reveal more of the flow structure than the results in [1]. In particular, we determine the shape of the plug region during breaking. We also investigate larger amplitude wall perturbations at significant Bingham numbers, B. Here we show that a unyielded plug begins to form on the wall in the widest part of the channel, at a critical amplitude. It is not apparently necessary for the plug to break, since the static wall-layer blocks the channel allowing a faster plug velocity at the channel centre, which reduces the stresses. Refs: [1] Ryan & Frigaard [2] Saramito [3] Lipscomb & Denn Time and Date: 4:10--5:00 p.m., Thursday, November 10, 2005 Event: SFU/UBC Number Theory Seminar at SFU Speaker: Peter Borwein, SFU Subject:The Riemann Hypothesis - not necessarily for experts'' Location: SFU Campus, Room ASB 10900 Time and Date: 3:00--4:00 p.m., Monday, November 14, 2005 Event: IAM Seminar Series Speaker: Peter Berg, Faculty of Science, University of Ontario Institute of Technology Subject:Linking Cellular Automata and Optimal-Velocity Traffic Models through Wave Selections at Bottlenecks'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Cellular automata (CA) models have been widely used to simulate traffic flow on highways and road networks, in particular the Nagel-Schreckenberg (NS) model. Together with car-following and continuum models, they represent the three most popular classes of traffic models. In this talk, we will investigate a bottleneck simulation of road traffic on a loop, using the NS model. Three types of stationary wave solutions emerge. They consist of: a. two shock waves at the bottleneck boundaries, b. one shock wave at the boundary and one on the 'open' road, and c. the trivial solution, i.e. homogeneous uniform flow. These solutions are selected dynamically from a range of kinematically possible solutions. This is similar in fashion to the wave selection in a bottleneck simulation of the optimal-velocity (OV) car-following model, a coupled system of ODEs. It is also one of the strongest indications to-date that CA and OV models share certain underlying dynamics, although the former are discrete in space and time while the latter are continuous. Time and Date: 12:30--2:00 p.m., Tuesday, November 15, 2005 Event: UBC SCAIM Seminar Speaker: Evgeny Sorkin, Department of Physics & Astronomy, UBC Subject:Critical collapse of a scalar field in higher dimensional spacetime'' Location: MATX 1118 Abstract: The scaling phenomenon found in general relativistic critical gravitational collapse of a massless scalar field is extended to higher dimensions. We find that in the range 4 <= D <= 11 of the spacetime dimension the behavior is qualitatively similar to that originally discovered by Choptuik in 4D, back in 1992. In each dimension we obtain numerically the universal numbers associated with the critical collapse: the scaling exponent gamma and the echoing period Delta. The behavior of these numbers with increasing dimension seems to indicate that gamma reaches a maximum and Delta a minimum value around 11 <= D <= 13. These results and their relation to the phase transition in the higher-dimensional black hole--black string system are discussed. Time and Date: 3:30--4:30 p.m., Tuesday, November 15, 2005 Event: Joint SFU/UBC Discrete Math/Computer Science Theory Seminar. Cancelled Nov. 14th due to illness. Speaker: John Bueti, UCLA Subject:A combinatorial result for the (n,k) problem'' Location: WMAX 216 (PIMS Seminar Room), 1933 West Mall, UBC Abstract: The (n,k) problem is a variant of the Kakeya problem which asks one to determine a lower bound on the size of a set E contained in the vector space F^n (for some large finite field F) which has the property that E contains a translate of every k-dimensional subspace of F^n. In this talk, we will discuss a bound for the associated maximal function operator whose proof depends entirely upon incidence combinatorics. Time and Date: 3:30 p.m., Tuesday, November 15, 2005 Event: DG-MP-PDE Seminar Speaker: Nataliya Ivanova, Department of Mathematics, UBC Subject:On symmetry properties of nonlinear Schrodinger equations'' Location: WMAX 110 (PIMS Seminar Room) Abstract: The complete group classification in the class of Schrodinger equations with power nonlinearity and potential term is performed. We construct all possible inequivalent potentials for which these equations have non-trivial Lie symmetries. All admissible transformations in the class under consideration are found. The obtained results are used to derive some results on existence and uniqueness of solutions of Cauchy problem. Time and Date: 4:00 p.m., Tuesday, November 15, 2005 Event: Algebraic Geometry Seminar Speaker: Vladimir Chernousov, University of Alberta Subject:Motivic decomposition of projective homogeneous varieties and the Krull-Schmidt theorem'' Location: MATX 1118 Abstract: We discuss the problem of decompositon of a motive of the product of two projective homogeneous G-varieties into a direct sum of twisted motives of projective homogeneous G-varieties and uniqueness of such decompositions. Time and Date: 2:00 p.m., Wednesday, November 16, 2005 Event: Mathematical Biology Seminar Speaker: Neil Balmforth, UBC Subject:Locomotion of Gastropods: Lubrication theory plus RoboSnail'' Location: WMAX 216 (PIMS) Abstract: Many gastropods, such as slugs and snails, crawl via adhesive locomotion in which the foot sends waves over a fluid layer between the creature and the underlying surface. We investigate this method of propulsion using two mathematical models, one for direct waves and one for retrograde waves. We then test the effectiveness of both proposed mechanisms by constructing two mechanical crawlers. Each crawler uses a different mechanical strategy to move on a thin layer of fluid. The first uses a flexible flapping sheet to generate lubrication pressures in a Newtonian fluid which in turn propels the mechanical snail. The second generates a wave of compression on a layer of Laponite, a non-Newtonian, finite-yield stress fluid with characteristics similar to those of snail mucus. This second design can climb smooth vertical walls and perform an inverted traverse. Time and Date: 2:00--3:00 p.m., Wednesday, November 16, 2005 Event: Mathematics Colloquium hosted by PIMS & UBC Speaker: Heinz Bauschke, UBC Okanagan Subject: Projection methods - a guided tour'' Location: MATH 103 Please plan to attend the PIMS hosted Tea and refreshments after the colloquium in WMAX 101. Time and Date: 2:45--3:35 p.m., Wednesday, November 16, 2005 Event: PIMS Tea Location: WMAX 101 (PIMS Library) Time and Date: 3:30 p.m., Wednesday, November 16, 2005 Event: Algebra Topology Seminar Speaker: Dale Rolfsen, UBC Subject:The Poincare conjecture and its cousins'' Location: WMAX 110 Abstract: For a hundred years, topologists have attacked the PC, sometimes by finding equivalent algebraic or topological conjectures, which might "reduce" the problem. Now that the PC has (reputedly) been solved by a differential geometer, some of these other problems are also solved -- the reverse of the expected order of things. And some are not. My talk will be a survey of some of these "cousins" of the PC. Time and Date: 3:30--4:30 p.m., Wednesday, November 16, 2005 Event: Probability Seminar Speaker: Rick Durrett, Cornell University Subject:Waiting for ATCAAAG'' Location: WMAX 216 Abstract: One possible explanation for the substantial organismal differences that have developed in the 6 million years sincee the divergence of humans and chimpanzees is that there have been changes in gene regulation. The word in the title is a sample transcription factor binding sites and motivates the following probability question: given a 1000 nucleotide region in our genome, how long does it take for a specified six to nine letter word to appear in that region in some individual? Stone and Wray (2001) computed 5949 years as the answer for six letter words in the human population. We will show that for words of length 6, the average waiting time is 100,000 years while for words of length 8, the waiting time is roughly a 1/3 - 2/3 mixture of exponentials with means 375,000 years and 625 million years. In biological reality, the match to the target word does not have to be perfect for binding to occur. If we model this by saying that we allow mismatch, then almost all of the mass in the probability distribution shifts to the smaller mean. This is joint work with Deena Schmidt. Time and Date: 4:00 p.m., Wednesday, November 16, 2005 Event: IAM Student-Faculty Seminar Speaker: Shreyas Mandre, Department of Mathematics, UBC Subject:Pouring things down an incline and related flows'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: It is common knowledge that water runs down an incline, so do other liquids. But as they flow down, I will begin by show some interesting things that may happen, followed by a discussion on the motivation for studying such flows. One of the observations on such flows is the propagation of waves and I will briefly explain the mechanism behind their formation. The problem of flow down an incline is related to a few others, for example the flow of air past vocal cords generating speech. For the second part, I will allude to the mechanism of processes like speech generation in somewhat detail and conclude by mentioning some future work and open problems. Time and Date: 4:00--5:00 p.m., Thursday, November 17, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker: Biao Wu, School of Mathematics and Statistics, Carleton University Subject:Interacting Systems in Time-varying and Random Environments'' Location: WMAX 216 Abstract: Two topics of interacting systems will be covered in this talk: A) multiagent models and B) interacting agent feedback finance models. In the multiagent models, there exist a closed system of N agents who are classified into r types with respect to their states of an internal system. Each agent can change its type by its observation of the performances of the internal states or by the relative frequency of different internal states among the others (the latter is called multinomial sampling, which is one source of interaction). The multiagent models with multinomial sampling are related to the Wright-Fisher model. The asymptotic behavior of multiagent models are studied by the weak convergence criteria for time-inhomogeneous Markov processes and the theory of Volterra integral equations of the second kind. In addition to the assumptions of multiagent models, we assume in the interacting agent feedback finance models that there is a financial asset and there exists a recursive log price mechanism. The change of the types of agents is based on the empirical distribution of the types of agents as well as the market price of the financial asset. The market price has an influence, feedback, on the change of the internal states of agents. There are two kind of interactions among agents: the effect of the empirical distribution of the agents' types and the feedback of market price on the switching of an agent's type. The weak convergence criteria for time-inhomogeneous Markov processes and the theory of nonlinear Volterra equations of second kind with semi-Lipschitz conditions are employed to analyze the asymptotics of interacting agent feedback finance models. One simple example will be given to illustrate the link between the interacting agent feedback finance models in random environments and the geometric Brownian motion of stock price forumula suggested by Samuelson. Time and Date: 4:00--5:00 p.m., Thursday, November 17, 2005 Event: Graduate Student Seminar Speaker: Jesse Goodman, Department of Mathematics, UBC Subject:Conformal invariance and the restriction property'' Location: MATX 1102 Abstract: Many two-dimensional random processes (including Brownian motion) are conformally invariant: when run in two different subdomains of C, the resulting curves are related by a conformal map. Using a blend of complex analysis and probability, recent work has classified all conformally invariant processes that also satisfy the chordal restriction property. The talk will explain the restriction property and discuss connections with reflected Brownian excursions, Brownian bubbles, and the Schramm-Loewner evolution (SLE). Time and Date: 4:00--5:00 p.m., Thursday, November 17, 2005 Event: Complex Fluids Seminar Speaker: Speaker: Mark Jellinek, Department of Earth and Ocean Sciences, UBC Subject:Are Earth-like mantle plumes weird: The improbable longevity of hotspots and mantle plumes'' Location: MATH 225 Abstract: The existence, spatial distribution and style of volcanism on terrestrial planets is an expression of their internal dynamics and evolution. On Earth, a physical link has been proposed between hotspots, regions with particularly persistent, localized, and high rates of volcanism, and underlying deep mantle plumes from the core-mantle boundary. Such mantle plumes are thought to be constructed of large spherical heads and narrow trailing conduits. This plume model has provided a way to interpret observable phenomena including the volcanological, petrological and geochemical evolution of ocean island volcanoes, the relative motion of plates, continental breakup, global heat flow and the Earth's magnetic field within the broader framework of the thermal history of our planet. Despite the plume model's utility the underlying dynamics giving rise to hotspots as long-lived stable features in a convecting mantle have remained elusive. In this talk I combine results from new and published observational, analog, theoretical and numerical studies to address two key questions: --Why might mantle plumes in the Earth have a head-tail structure? --How can mantle plumes and hotspots persist for large geological times? I show first that the characteristic head-tail structure of mantle plumes, which is a consequence of hot upwellings having a low viscosity, is likely a result of strong cooling of the mantle by large-scale stirring driven by plate tectonics. Second, I show that the head-tail structure of such plumes is a necessary but insufficient condition for their longevity. Third, I summarize seismological, geodynamic, geomagnetic and geochemical constraints on the structure and composition of the lowermost mantle to argue that the source regions for most deep mantle plumes contain dense, low viscosity material within the D'' layer at the base of the Earth's mantle. Such a layer may be composed of partial melt, outer core material or a mixture of both (i.e. a "dense layer"). Fourth, using results from laboratory experiments on thermochemical convection and theoretical scaling analyses, I will argue that the longevity of mantle plumes in the Earth is a consequence of interactions between plate tectonics, core cooling and dense, low viscosity material within D''. Conditions leading to Earth-like mantle plumes and hotpsot volcanoes are highly specific and may, thus, be unique to our own planet. Time and Date: 2:00--3:00 p.m., Friday, November 18, 2005 Event: Special Information Theory Seminar Speaker: Gadiel Seroussi, Mathematical Sciences Research Institute, Berkeley, CA Subject:On Universal Types'' Location: WMAX 110 (PIMS Seminar Room), 1933 West Mall, UBC Abstract: The universal type class of a sequence x^n is defined, in analogy to the notion underlying the classical method of types. Two sequences of the same length are said to be of the same universal (LZ) type if and only if they yield the same dictionary (or, equivalently, parsing tree) in the incremental parsing of Ziv and Lempel (1978). It is shown that for any finite order k, the variational distance between the kth order empirical probability distributions of two sequences of the same universal type vanishes as the sequence length tends to infinity. Consequently, for any k, and any kth order probability assignment, the difference between the normalized logarithms of the probabilities assigned to two sequences of the same universal type also vanishes asymptotically. The size of a universal type class is studied, and it is shown that its asymptotic behavior parallels that of the conventional counterpart, with the LZ78 code length playing the role of the empirical entropy. The number of universal types for sequences of length n is estimated, and shown to be of the form \exp((1+o(1))\gamma n/\log n) for a well characterized constant \gamma. Algorithms for enumerating the sequences in a universal type class, and for drawing a sequence from the class with uniform probability are described. As an application, the problem of universal simulation of individual sequences is considered. A sequence drawn with uniform probability from the universal type class of x^n is an optimal simulation of x^n in a well defined mathematical sense. Time and Date: 3:00 p.m., Friday, November 18, 2005 Event: Mathematics Colloquium Speaker: Vladimir Chernousov, University of Alberta Subject: Essential dimensions of algebraic groups'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, November 21, 2005 Event: IAM Seminar Series Speaker: Ulrich Horst, Department of Mathematics, UBC Subject:Queuing theoretic approaches to financial price fluctuations'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: We establish a central limit theorem for queuing models where the arrival and departure rates depend on stationary semi-Markov processes with heavy tailed sojourn time distributions. We show that after suitable rescaling the fluctuations around the deterministic first order approximation can be described by a fractional Ornstein-Uhlenbeck process. We apply our limit theorem to model price fluctuations in financial markets with many inert investors that trade only occasionally. With our choice of scaling long range dependence emerges in financial time series. We also link investor inertia to the observed fall is the Hurst coefficient of the S&P 500 index over the late 1990s. The talk is based on joint work with E. Bayraktar (Michigan) and R. Sircar (Princeton). Time and Date: 3:00 p.m., Monday, November 21, 2005 Event: Algebraic Geometry Seminar Speaker: Tonny Springer, University of Utrecht Subject:Some subvarieties of a compactification of a semisimple group'' Location: WMAX 110 (PIMS Seminar Room) Abstract: An adjoint semisimple group G over an algebraically closed field has a "wonderful" compactification X (introduced by De Concini and Procesi). X is a smooth projective G\times G-variety which contains G as an open stable subvariety, G\times G acting on G in the well-known way. The closures in X of familiar subsets of the group G are interesting subvarieties of X. Examples of such subsets are: double cosets BwB (B a Borel subgroup) and regular conjugacy classes. In the talk I will discuss a number of recent results about the geometry of their closures. Time and Date: 4:00 p.m., Monday, November 21, 2005 Event: Mathematics Colloquium Speaker: Peter Walters, University of Warwick Subject: Cohomology for Subshifts'' Location: MATH 104 Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 12:30--2:00 p.m., Tuesday, November 22, 2005 Event: UBC SCAIM Seminar Speaker: Joab Winkler, Department of Computer Science, University of Sheffield Subject:The stability of the effective condition number for least squares problems'' Location: MATX 1118 Abstract: The condition number of the linear algebraic equation Ax=b, where A is n x n and non-singular, may overestimate its exact normwise condition number S(A,b), and this was the motivation for Chan and Foulser to introduce a sequence S(A,b;k), k=1,...,n, of upper bounds of S(A,b)in 1988. It is shown that although the minimum upper bound is a very good approximation to S(A,b), it is ill-conditioned when the equation is truly ill-conditioned, that is, when S(A,b) >> 1. This result is established theoretically for the normal equations that arise in least squares problems, and it is confirmed computationally by considering an example of regression using radial basis functions. It is in agreement with the result of Demmel in 1987, which states that the computation of the numerical condition of a problem is approximately as difficult as the computation of its solution. Time and Date: 3:30--4:30 p.m., Tuesday, November 22, 2005 Event: Joint SFU/UBC Discrete Mathematics and Theoretical Computing Science Seminar Speaker: Pavol Hell, School of Computing Science, SFU Subject:From Graph Colouring to Constraint Satisfaction: There and Back Again'' Location: SFU Campus, IRMACS Theatre Abstract: I will discuss dichotomies in graph colouring, homomorphism, and constraint satisfaction problems, and introduce a concept of fullness of constraint satisfaction problems. When this concept is applied to graph colourings, we obtain interesting graph partition problems, which frequently arise in the study of perfect graphs. Emphasis will be on forbidden subgraph characterizations (if time permits). Time and Date: 3:30 p.m., Tuesday, November 22, 2005 Event: DG-MP-PDE Seminar Speaker: Alan Hammond, Department of Mathematics, UBC Subject:Moment bounds and gelation in PDE modelling coaslescence'' Location: WMAX 110 (PIMS) Abstract: We examine the behaviour of solutions to a system of PDE (the Smoluchowski PDE), that model the aggregation of mass-bearing particles that diffuse and are prone to coagulate in pairs at close range. Conditions under which these solutions conserve mass for all time will be presented, along with stronger estimates, moment bounds that show that heavy particles are rare. In the case where mass conservation fails, a gelation occurs at a finite time, with particles coalescing to such a degree that some develop infinite mass. Many of the estimates have been derived both by PDE methods and by a probabilistic one. I'll give examples of each type. This is joint work with Fraydoun Rezakhanlou. Time and Date: 2:00 p.m., Wednesday, November 23, 2005 Event: Mathematical Biology Seminar Speaker: Fred Brauer, Department of Mathematics, UBC Subject:Simple pandemic models'' Location: WMAX 216 (PIMS) Abstract: Stochastic simulation of large network models have become the standard approach to modelling epidemics and control measures, including anticipated possible pandemics. We show that simple compartmental deterministic models can give some of the predictions of such models simply and with better understanding of critical dependence on some parameters. In particular, the dependence on the initial number of infectives is critical, and this makes predictions of the amount of treatment needed for control and the number of disease cases completely unreliable. However, comparison of different control strategies is still possible. (work joint with Julien Arino, Pauline van den Driessche, James Watmough, and Jianhong Wu). Time and Date: 3:30 p.m., Wednesday, November 23, 2005 Event: Algebra Topology Seminar Speaker: Tonny Springer, University of Utrecht Subject:Some subvarieties of a compactification of a semisimple group II'' Location: WMAX 110, Note: This is a continuation of Monday's Algebraic Geometry Seminar. Time and Date: 3:30--4:30 p.m., Wednesday, November 23, 2005 Event: Probability Seminar Speaker: Codina Cotar, Department of Mathematics, UBC Subject:Edge reinforced random walk as a random walk in random environment'' Location: WMAX 216 Abstract: We consider linear edge reinforced random walk on a finite graph. This was studied by S. Rolles and M.S.Keane, who developed the so called "magic formula", expressing a linear edge reinforced random walk as a random walk in a random environment. By using properties of the gamme function, a new equivalent formula is developed. Time and Date: 4:00 p.m., Wednesday, November 23, 2005 Event: IAM Student-Faculty Seminar Speaker: Miguel Angel Moyers-Gonzalez, Department of Mathematics, UBC Subject:Transient effects in oilfield cementing flows'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: A two-dimensional evolution model for displacement flows occurring in the primary cementing of an oil well is presented. This process involves displacement of a sequence of non-Newtonian fluids along a narrow eccentric annulus. It has been shown that for certain rheological and physical parameters of the fluids, the displacement front will advance much faster on the wide side of the annulus than on the narrow side. In extreme cases the displacement front does not advance at all on the narrow side of the annulus and a static mud channel results as the finger advances up the wide side. We consider whether the interface of a progressively advancing finger will remain stable to small perturbations and also investigate how a mud channel might be removed by pulsation of the flow rate, which is sometimes used in the cementing industry. Time and Date: 3:00--3:50 p.m., Thursday, November 24, 2005 Event: SFU/UBC Number Theory Seminar at UBC Speaker: Yoonjin Lee, SFU Subject:The structure of the class groups of global function fields of any unit rank'' Location: UBC Campus, WMAX 110 (PIMS Seminar Room), 1933 West Mall Abstract: The problem of determining the structure of the class group dates back to Gauss. In this talk we discuss the structure of the class groups of global function fields. Let F be a finite field and T a transcendental element over F. We show an explicit method of constructing, for positive integers m,n, and r with 0 â r â m-1, infinitely many global function fields K of degree m over F(T) such that K has a given unit rank r and the ideal class group of K contains a subgroup isomorphic to (Z/nZ)^{m-r}. Time and Date: 4:00--5:00 p.m., Thursday, November 24, 2005 Event: PIMS-MITACS Math Finance Seminar Speaker: Tahir Choulli, Department of Mathematical & Statistical Sciences, University of Alberta Subject:Minimal Hellinger martingale measures of order q'' Location: WMAX 216 Abstract: In my talk I will propose an extension of the minimal Hellinger martingale measure (MHM hereafter) concept to any order q\not=1 and to the general semimartingale framework. This extension allows us to provide a unified formulation for the minimal martingale measure of F\"ollmeer and Schweizer (here q=2), the minimal Hellinger martingale measure of Grandits (here q=1/2), and the minimal distance martingale measure when the utility is logarithmic (here q=0). Under some mild conditions of integrability and arbitrage, we show the existence of the MHM measure of order q, and we describe it explicitly in terms of pointwise equations in \RR^d. Application to the maximization of expected power utility at stopping times with implied liability or endowment is given. We describe an optimal investment that is robust with respect to the investor's lifetime (which could be certain or announced at birth). Finally the main results of the paper are illustrated for the discrete-time market models, where a relationship between this optimal martingale measure and a dynamic risk measure is established as well. This talk is based on a joint paper with Christophe Stricker and Jia Li. Time and Date: 4:00--5:00 p.m., Thursday, November 24, 2005 Event: Complex Fluids Seminar Speaker: Dana Grecov, Department of Mechanical Engineering, UBC Subject:Modeling Microstructural Processes in Liquid Crystalline Flows'' Location: MATH 225 Abstract: The orientational order of liquid crystal materials offers a unique pathway to create new nano- and micro-structures with unique optical, electromagnetic, and mechanical properties. Nematic liquid crystalline materials are textured, anisotropic, viscoelastic materials. Their mechanical behavior is greatly influenced by the presence of textures, or spatial distribution of topological defects. We present a multiscale theory and simulation of hydrodynamic texture formation to provide fundamental principles for control and optimization of structures in liquid crystal materials. We characterize the relation between rheological functions and textural transformations of flow-aligning liquid crystalline materials subjected to shear start-up flow. Defects reduce stress so that when defects leave the system, the shear stress increases. Simulated textural transformations show that smooth staircase stress growth is the result of defect annihilation processes. The non-monotonic stress growth is consistent with experimental observations. Simulated textures provide specific important knowledge to the understanding of the rheology of textured liquid crystalline materials. Time and Date: 4:10--5:00 p.m., Thursday, November 24, 2005 Event: SFU/UBC Number Theory Seminar at UBC Speaker: Stephen Choi, SFU Subject:Why Lehmer's conjecture is so difficult'' Location: UBC Campus, WMAX 110 (PIMS Seminar Room), 1933 West Mall Abstract: We compute asymptotic formulas for mean values of Mahler's measure and the Lp-norms of several classes of polynomials with restricted coefficients and bounded degree. We study the unimodular polynomials with complex coefficients of modulus 1, the Littlewood polynomials with {-1,1} coefficients, the height-1 polynomials with {-1,0,1} coefficients, and their restrictions to reciprocal polynomials. We show for instance that both the geometric mean and the arithmetic mean of Mahler's measure of the unimodular polynomials with degree n-1 approach e^{-Î³/2}n^{1/2} as n grows large, and that this same result holds for the Littlewood polynomials. Moreover, we prove that the normalized measure or Lp-norm of a polynomial in one of these families lies arbitrarily close to the corresponding mean value with probability approaching 1 as the degree grows large. Time and Date: 3:00 p.m., Friday, November 25, 2005 Event: Mathematics Colloquium Speaker: Ivar Ekeland, PIMS, UBC Subject: Nuts, bolts, and markets'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, November 28, 2005 Event: IAM Seminar Series Speaker: James J. Feng, Department of Mathematics and the Department of Chemical and Biological Engineering, UBC Subject:Recent Adventures on Interfaces of Simple and Complex Fluids'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: I will report recent results from our group on experimental and computational studies of interfacial dynamics of Newtonian and viscoelastic fluids. The experimental work has centered on the coalescence between a drop and a fluid-fluid interface, where a phenomenon known as 'partial coalescence' takes place within proper ranges of the Ohnesorge number. We have identify the mechanisms governing this process for Newtonian and polymeric liquids. On the numerical side, we have successfully reproduced the experimental observations of partial coalescence. In addition, I will also discuss simulations of the formation and dispersion of droplets in microfluidic channels. Time and Date: 3:00 p.m., Monday, November 28, 2005 Event: Algebraic Geometry Seminar Speaker: Kiumars Kaveh, UBC Subject:Canonical bases and toric degeneration of flag and spherical varieties'' Location: WMAX 110 (PIMS Seminar Room) Abstract: I will briefly introduce Kashiwara-Lutzig canonical basis and its string parametrization due to Littleman, Bernstein and Zelevinsky. I then show how the combinatorics of string parametrization can be used to prove that the homogeneous coordinate ring of a flag variety has a so-called SAGBI basis. This will imply that a flag variety can be flatly degenerated to a toric variety. This result extends to the more general case of spherical varieties. Time and Date: 3:30 p.m., Tuesday, November 29, 2005 Event: DG-MP-PDE Seminar Speaker: Claudio Fernandez, Pontificia Universidad Catolica de Chile Subject:Absence of embedded eigenvalues for perturbed Hamiltonians'' Location: WMAX 110 (PIMS) Abstract: We shall show how to use a technique, based on commutator estimates, to prove that the propagator U(t,0) for a self-adjoint operator H(t)=H_0+V(t), has no eigenvalues, with adequate conditions on the potential V. Secondly, we consider the Stark magnetic Hamiltonian, H(\mu ,\epsilon )=(D_x-uy)^2+D_y^2+\epsilon x+V(x,y), on the Hilbert space L^2(\mathbb R^2). We show that if the potential V satisfies some mild regularity conditions and it is sufficiently decaying at infinity, then the operator H has no eigenvalues. Time and Date: 2:00 p.m., Wednesday, November 30, 2005 Event: Mathematical Biology Seminar Speaker: Muhammad Arshad Chaudhry, Michael Smith Laboratories, UBC Subject:Influence of Culture pH and Osmolality on the Maintenance of Pluripotentiality of Murine Embryonic Stem Cells'' Location: WMAX 216 (PIMS) Abstract: The clinical realization of stem cells based gene and tissue regeneration therapies depends on the development of consistent, robust and scalable processes to expand their numbers without compromising their developmental potential. Murine embryonic stem (ES) cells provide a practical model for stem cell culture process research as they can be readily obtained at relatively high numbers and purities. Conventional ES cultures require daily medium exchange and an understanding of their environmental tolerance ranges is still lacking. We have now begun to explore these using a functional assay (Embryoid body, EB, formation) to quantify the integrity of an ES cell line, R1, exposed to various culture stresses. Based on the EB formation assay, culture environment strongly influences the developmental potential of two ES cell lines, R1 and EFC. A dose-response analysis of R1 cells exposed to various medium pH and osmolalities was carried out and revealed that within 48 h, the yield of EBs was ~ 3-fold decreased (p<0.05) when R1 cells were cultured in pH 7.0 or 400 mOsm/kg osmolality medium (compared to a pH of 7.3 and 300 mOsm/kg osmolality). This was due to both a relative and absolute decreases in the rate of EB-forming cell expansion. These studies provide guidance in determining the optimal culture conditions and environmental tolerances for stem cell bioprocess research and development. Time and Date: 3:30 p.m., Wednesday, November 30, 2005 Event: Algebra Topology Seminar Speaker: Alejandro Adem, PIMS & UBC Subject:Products in the Cohomology and K-theory of Orbifold'' Location: WMAX 110 Abstract: We will discuss products in the cohomology and K-theory of orbifolds, as well as a twisted version for certain cocycles. Time and Date: 4:00 p.m., Wednesday, November 30, 2005 Event: IAM Student-Faculty Seminar Speaker: Livio Gibelli, Postdoctoral Fellow, Department of Mathematics, Milan Polytechnic, Italy Subject:Elements of kinetic theory" Location: LSK 301 Abstract: The talk will give a brief overview of the basic elements of the kinetic theory of gases. The purpose of kinetic theory is to model the time evolution of a collection of particles. The particles may be entirely different objects depending on the physical situation. For instance, the particles are molecules in a neutral gas, electrons and ions in a plasma, stars in stellar dynamics, galaxies or even clusters of galaxies in cosmological problems. Mathematical models of particle systems are most frequently described by kinetic or fluid equations. The connection between the two approaches will be stressed. The time evolution of the system is determined by the nature of interactions between the particles. The cases in which the driving mechanisms are collisions (the Boltzmann equation) and interaction through electromagnetic fields (the Vlasov-Maxwell system) will be briefly discussed. Time and Date: 3:30 p.m., Thursday, December 1, 2005 Event: DG-MP-PDE Seminar Speaker: Andrew Comech, Texas A & M University Subject:Global attractor for the Klein-Gordon equation with a nonlinearity supported at a point'' Location: WMAX 110 (PIMS) Abstract: We consider the long-time asymptotics of all finite energy solutions to the Klein-Gordon equation in one dimension, with the nonlinearity concentrated at a point. Our main result is that the attracting set of any finite energy solution consists of nonlinear eigenfunctions'', also known as solitary or standing waves. The problem is inspired by Bohr's postulate on quantum transitions and Schroedinger's identification of the quantum stationary states to the eigenfunctions of the coupled Maxwell-Schroedinger or Maxwell-Dirac equations. This is a joint work with Alexander Komech, Vienna University. Time and Date: 4:00--5:00 p.m., Thursday, December 1, 2005 Event: Graduate Student Seminar Speaker: Mat Rogers, Department of Mathematics, UBC Subject:A brief introduction to Mahler Measure'' Location: MATX 1102 Abstract: In this talk I will give a brief introduction to Mahler measure, and I will discuss a few of my recent results. Recall that the Mahler measure of a n-dimensional polynomial, P(x1,...xn), is defined by the n-dimensional integral, m(P(x1,...,xn))=\int\log|P(z1,...zn)|/(z1*...*zn) dz1...dzn, where the path of integration is taken over T^n. When n>=2, we can find identities expressing Mahler measures in terms of L-functions. For example, I recently showed that, m(x+(1+x)^2+(1+x+y)^2 z)=28/5*Zeta(3)/Pi^2+Log(Phi), where Phi=(1+5^(1/2))/2 is the golden-ratio, and Zeta(3)=1+1/2^3+1/3^3.... I will discuss several results of this type. Time and Date: 4:00 p.m., Thursday, December 1, 2005 Event: Complex Fluids Seminar Speaker: Isaias Ochoa, Dept. of Chemical Engineering, UBC Subject:Paste extrusion of Polytetrafluoroethylene (PTEE) fine powder resin: The effects of the processing aid physical properties'' Location: MATH 225 Abstract: The rheological properties of a number of polytetrafluoroethylene (PTFE) pastes were studied relevant to paste extrusion process. The effects of the physical properties of lubricants and the geometrical characteristics of the extrusion die on the performing, extrusion pressure and mechanical properties of the final extrudates were also examined. A number of lubricants were characterized in terms of both flow and surface properties and identified as suitable for the paste extrusion of polytetrafluoroethylene (PTFE). The flow and surface properties of some lubricants were altered to study their relative effects on preforming and extrusion of PTFE paste. Based on this study, it was concluded that preforming quality increases with increase of lubricant viscosity and with improvement in the wettability characteristics of the lubricant with PTFE. The effects of the lubricant physical properties on the processing of polytetrafluoroethylene (PTFE) fine powder resins were also studied. It was found that the wettability (surface tension) and the viscosity of the lubricant play a significant role in the process as they strongly affect the pressure needed to extrude the PTFE pastes. These effects of the physical properties on the extrusion pressure influence significantly the mechanical properties of the final extrudates since the degree of fibrillation is strongly related to the extrusion pressure. The effects of die geometry as well as the extrusion temperatureon on extrusion pressure and mechanical properties of extrudates were also assessed in order to determine the geometrical characteristics and operation conditions for the optimization of the process. Finally, rheological characterization studies of the paste and the extrudates were performed in an attempt to clarify the behaviour of such an amazing material. Time and Date: 3:00 p.m., Friday, December 2, 2005 Event: Mathematics Colloquium Speaker: Maciej Zworski, UC Berkeley Subject: Counting states in wave mechanics'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, December 5, 2006 Event: Algebraic Geometry Seminar Speaker: Patrick Brosnan, Department of Mathematics, UBC Subject:Jumps in the height of the Hain-Reed biextension line bundle over the moduli space of curves'' Location: MATX 1102 Abstract: Using Hodge theory, Richard Hain and David Reed have defined a natural metrized line bundle B on the moduli space of curves. Hain and Reed showed that B extends with its metric to the moduli space of stable curves with compact type. However, Greg Pearlstein and I have shown that the metric of B is singular on certain strata of non-compact type in the boundary of the moduli space of stable curve. Our measure of singularity of the metric boils down to an invariant the degeneration of a variation of mixed Hodge structure which we call the jump. I plan to explain B, it's metric and our calculation of the jump. Time and Date: 3:30--4:30 p.m., Monday, December 5, 2005 Event: Probability Seminar **Cancelled** Speaker: Burgess Davis, Purdue University Subject:Continuous time vertex reinforced random walk'' Location: WMAX 216 (PIMS) Abstract: I will talk about joint work with Stas Volkov concerning a nearest neighbor random walk on graphs. On the integer lattice the walk is defined as follows. Initially the weight of each integer is one. The walk jumps to each of its neighbors at a rate proportional to the weight of that neighbor. The weight of an integer at time t is the time up to t that the walk has spent at the neighbor. So for example, the first jump is equally likely to be to either neighbor and the time T before this jump is exponential rate 2, while the second jump is exponential rate 2+a if T=a. The integers visited by this walk up to time t are asymptotically the interval (-clogt, clogt) where c is explicitly given. On some regular trees the walk goes to infinity while on others it visits every vertex. Time and Date: 12:30--2:00 p.m., Tuesday, December 6, 2005 Event: UBC SCAIM Seminar Speaker: Wayne Hayes, Department of Computer Science, UC Irvine Subject:From Butterflies to Galaxies: reliable simulation of chaotic systems'' Location: CS X736 Note: This is an alternate location (7th floor of new CS building). Abstract: The "Butterfly Effect" refers to the idea that a butterfly flapping its wings in Hawaii can affect the weather over Vancouver a few weeks later. The Butterfy Effect is an example of "sensitive dependence on small changes", which is exhibited by many nonlinear dynamical systems from integrated circuits to galaxies. When such systems are simulated on a computer, this sensitivity causes small numerical errors to become exponentially magnified, leading to the possibility that trajectories of such simulations are the result of nothing but magnified noise. To justify the reliability of such simulations, we turn to the study of "shadowing". A "shadow" is an exact trajectory that stays close to a numerical trajectory for a long time, even in the face of sensitive dependence. From the standpoint of physics, a numerical trajectory that has a shadow can be viewed as an experimental observation of that shadow, which means that the dynamics observed in the simulation are real. This is a very strong statement of simulation reliability. However, verifying the existence of a shadow formally takes time O(N^3), where N is the number of components in the system. In this talk I will outline how I demonstrated the existence of shadows of galaxy simulations in which N=10^8. Time and Date: 3:30 p.m., Tuesday, December 6, 2005 Event: DG-MP-PDE Seminar Speaker: Alexei Cheviakov, Department of Mathematics, UBC Subject:Framework for potential systems and nonlocal symmetries: Algorithmic approach'' Location: WMAX 110 (PIMS) Abstract: For a given PDE system, one can construct extended hierarchies ("trees") of nonlocally-related PDE systems. Each system in an extended tree is equivalent, in the sense that the solution set for any system in a tree can be found from the solution set for any other system in the tree. Due to the equivalence of solution sets, any coordinate-independent method of analysis (qualitative, numerical, perturbation, etc.) can be applied to any system within the tree, and may yield simpler computations and new results that cannot be obtained when the method is directly applied to the given system. Nonlocal symmetries and new local and nonlocal conservation laws for a given PDE system can arise from any system in its extended tree. We construct extended trees for the systems of Planar Gas Dynamics and Nonlinear Telegraph equations. Using the described framework, we demonstrate a direct relation between Eulerian and Lagrangian descriptions of gas dynamics, and find new families of conservation laws and new nonlocal symmetries. The presented research was done in collaboration with George Bluman (UBC). Time and Date: 3:30--4:20 p.m., Tuesday, December 6, 2005 Event: Joint Discrete Mathematics - Theoretical Computing Science UBC/SFU Seminar Speaker: David S. Gunderson, University of Manitoba Subject:Sumsets, primes, and combinatorics'' Location: SFU Campus, ASB 10900, IRMACS Theatre Abstract: If A and B are sets of numbers, the set A+B=\{a+b:a\in A, b\in B\} is called a sumset. Many questions in combinatorial number theory focus on sumsets and primes or prime factorization. For example, one might ask how large can two sets be so that their sumset consists only of primes? (When A=\{1,7\} and B=\{4,6\}, the sumset A+B consists only of primes.) Some questions regarding sumsets and primes have been answered using only the pigeonhole principle, Ramsey theory, or extremal graph theory---with no properties of primes being used! The main theorem in this talk regards the parity of the number of factors in A, B, and A+B. Let \Omega(n) denote the number of prime factors (not necessarily distinct) of n. In 1999, Rivat, S\'ark\"ozy and Stewart proved a result regarding maximal cardinalities of sets A, B \subset\{1,\ldots,N\} so that for every a\in A and b\in B, \Omega(a+b) is even. In joint work with Christian Elsholtz (Royal Holloway, University of London) the Rivat-S\'ark\"ozy-Stewart theorem is strengthened in three ways: (1) The role of Liouville \lambda-function, given by \lambda(n)=(-1)^{\Omega(n)}, is generalized to all non-constant completely multiplicative functions f from the natural numbers to \{-1,1\}. (2) Their results are also extended to all possible parities of \Omega on A, B, and A+ B, and, (3) in each case, many' such pairs (A,B) exist. Time and Date: 2:00 p.m., Wednesday, December 7, 2005 Event: Mathematical Biology Seminar Speaker: Anmar Khadra, Department of Mathematics, UBC Subject:Modeling the Pulsatile and Synchronized Behaviour of GnRH Neurons'' Location: WMAX 216 Abstract: The hypothalamic GnRH (Gonadotropin Releasing Hormone) decapeptide is essential for reproductive processes in vertebrates. GnRH plays key roles in the onset and progression of reproductive maturation, and regulation of hormonal changes that occur during menstrual and estrous cycle. It mediates the reproductive system responses to seasonal or diurnal cues. In primates, GnRH is secreted from synchronized GnRH neurons in a pulsatile and episodic manner in the median eminence, e.g., in humans, the hormone is released approximately every 60 mins. This pulsatile and episodic pattern is crucial for normal reproductive function. The underlying mechanism of the GnRH pulse generator that is responsible for the episodic secretion of GnRH has yet to be established. It is clear, however, that GnRH neurons have an intrinsic capacity for the generation of pulsatile neurosecretion. Recent experiments revealed important details of the molecular events underlying the GnRH pulsatility. It has been shown that GnRH neurons express GnRH receptors allowing GnRH to exert an autocrine action on them. Krsmanovic et al., proposed a mechanism describing this autocrine effect via Calcium and cAMP. In this talk we will present a mathematical model which reflects the properties of the proposed mechanism. Furthermore, we illustrate how this hormone can act as an agent or a "diffusible mediator" that is responsible for coupling the GnRH neurons to generate synchronized release of itself. We also show the robustness of synchronization to variations in the properties of the GnRH neurons. Time and Date: 3:30 p.m., Wednesday, December 7, 2005 Event: Algebra Topology Seminar Speaker: Ian Hambleton, McMaster University Subject:Finite groups acting freely on products on spheres'' Location: WMAX 110 Abstract: We will present some details of new methods and results about which finite groups can act freely and smoothly on a product of spheres. Time and Date: 3:00--3:50 p.m., Thursday, December 8, 2005 Event: SFU/UBC Number Theory Seminar at SFU Speaker: Chris Sinclair, PIMS, SFU, UBC Subject:Determinants, Pfaffians and Volumes of Polynomials'' Location: SFU Campus, Room ASB 10900 Abstract: I will outline a method for computing certain volumes of polynomials of interest to number theorists, random matrix theorists, and physicists. Time and Date: 4:10--5:00 p.m., Thursday, December 8, 2005 Event: SFU/UBC Number Theory Seminar at SFU Speaker: Mat Rogers, Department of Mathematics, UBC Subject:Multivariable Mahler measures and related integrals'' Location: SFU Campus, Room ASB 10900 Time and Date: 3:00 p.m., Friday, December 9, 2005 Event: Mathematics Colloquium Speaker: Ian Hambleton, McMaster University Subject: Groups and Geometry'' Location: WMAX 110 (PIMS Seminar Room) Refreshments will be served at 2:45 p.m. (WMAX PIMS Lounge). Time and Date: 11:00 a.m., Wednesday, December 14, 2005 Event: Algebra Topology Seminar Speaker: Genevieve Walsh, U of Texas, Austin Subject:Surfaces in finite covers and the group determinant'' Location: WMAX 110 Abstract: We show that infinitely many fillings of any one-cusped hyperbolic three-manifold are virtually Haken. The main tool is a symmetrized version of the group determinant, as studied by Frobenius and Dedekind. I will explain what the group determinant is, and how it relates to this problem via the representation theory of finite groups. This is joint work with Daryl Cooper (UCSB). Time and Date: 2:00--3:00 p.m., Wednesday, December 14, 2005 Event: Mathematics Colloquium Speaker: Alexander Jones, University of Toronto Subject: Locus theorems in ancient Greek geometry'' Location: WMAX 110 (PIMS Seminar Room) Refreshments will be served at 1:45 p.m. (PIMS Lounge). Time and Date: 3:30 p.m., Wednesday, December 14, 2005 Event: Algebra Topology Seminar Speaker: Victor Nunez, CIMAT Subject:Universal Montesinos knots'' Location: WMAX 110 Abstract: An interesting way of constructing 3-manifolds is through the study of branched coverings and universal knots. Montesinos knots were, until recently, untractable in questions about universality. We explore the theory of universal knots, and review some known results. Using these and some new points of view, we show universality of many Montesinos knots. Time and Date: 11:00 a.m., Friday, December 16, 2005 Event: Algebra Topology Seminar Speaker: Rick Jardine, UWO Subject:Cocycle categories and gerbes'' Location: WMAX 110 Abstract: Cocycle categories are ubiquitous in homotopy theory, and their sets of path components represent morphisms in a large family of homotopy categories. The cocycle category approach is a flexible tool for demonstrating homotopy classifications results for equivalence classes of objects with structure. This approach can be used, in particular, to give homotopy classification results for locally connected stacks (aka. gerbes). It's not as scary as it sounds. Time and Date: 3:00--4:00 p.m., Friday, December 16, 2005 Event: Mathematics Colloquium Speaker: Ramesh Sreekantan, Tata Institute Subject: `Drinfeld Modular Curves and special values of L-functions'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. (Math Lounge).