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 Events
Department of Mathematics, University of California, Davis
Mon 3 Mar 2014, 3:00pm SPECIAL
Institute of Applied Mathematics
LSK 460
Phase Retrieval, Random Matrices and Convex Optimization (IAM-PIMS Distinguished Colloquium)
LSK 460
Mon 3 Mar 2014, 3:00pm-4:00pm

Abstract

Phase retrieval is the century-old problem of reconstructing a function, such as a signal or image, from intensity measurements, typically from the modulus of a diffracted wave.  Phase retrieval problems - which arise in numerous areas including X-ray crystallography, astronomy, diffraction imaging and quantum physics - are notoriously difficult to solve numerically.  They also pervade many areas of mathematics, such as numerical analysis, harmonic analysis, algebraic geometry, combinatorics, and differential geometry.  I will introduce a novel framework for phase retrieval, which comprises tools from optimization, random matrix theory, and compressive sensing. In particular, we will see that for certain types of random measurements a function, such as a signal or image, can be recovered exactly with high probability by solving a convenient semidefinite program without any assumption about the function whatsoever and under a mild condition on the number of measurements.  Our method, known as PhaseLift, is also provably stable vis-a-vis noise.  I will describe how this approach carries over to the classical phase retrieval setting using structured random illuminations.  I conclude with some open problems.

Note for Attendees

Refreshments start 15 minutes before the talk in the IAM Lounge, Room 306 of the LSK building.
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UBC
Mon 3 Mar 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Surjectivity and lifting the Weyl group action to the equivariant cohomology of a Springer fibre
ESB 4127 (host: UBC)
Mon 3 Mar 2014, 3:00pm-4:00pm

Abstract

A famous result of Springer says that the Weyl group of a reductive algebraic group G (over C) acts on the cohomology of the subvariety X_u of the flag variety G/B consisting of the flags fixed by a unipotent u in G. This result was unexpected since W does not act on X_u itself. Recently, Kumar - Procesi and Goresky - MacPherson showed that Springer's action lifts to the equivariant cohomology of X_u with respect to the maximal torus in C_G(u) for so called parabolic unipotents u with the proviso that the cohomology morphism j*: H*(G/B) \to H*(X_u) is surjective. In this talk we will describe the parabolic unipotents for which j* is surjective and indicate a direct proof of lifting. 
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Robert Fraser
UBC
Tue 4 Mar 2014, 2:00pm
Mathematical Education
Math 126
Comprehension of Arithmetic Word Problems: A Comparison of Successful and Unsuccessful Problem Solvers
Math 126
Tue 4 Mar 2014, 2:00pm-3:00pm

Abstract

Rob will present "Comprehension of Arithmetic Word Problems: A Comparison of Successful and Unsuccessful Problem Solvers", found here: http://citeseerx.ist.psu.edu/viewdoc/download?rep=rep1&type=pdf&doi=10.1.1.167.8370
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University of Victoria
Tue 4 Mar 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB2012 (PIMS)
Optimal Transport-based Model and Algorithms for Particle Image Velocimetry
ESB2012 (PIMS)
Tue 4 Mar 2014, 3:30pm-4:30pm

Abstract

Particle Image Velocimetry (PIV) is a technique using successive laser images of particles immersed in a fluid to measure the velocity field of the fluid flow. Traditionally, cross-correlation is employed to extract the field from each pair of recorded images. This talk will introduce a new approach based on Optimal Transport (OT) to approximate the velocity field. More specifically, we consider the solution of the L2 OT problem with initial and final densities given by successive images of tracers. We will first present a model for this situation and investigate the behaviour of the OT map with respect to the model's key parameters. Then, we will present some algorithms and numerical results applying this theory to synthetic and real examples. This is joint work with B.Khouider and M.Agueh.
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Peter Overholser
UAlberta
Wed 5 Mar 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
An introduction to the Gross-Siebert program (Part II)
ESB 4127 (host: UAlberta)
Wed 5 Mar 2014, 3:00pm-4:00pm

Abstract

 TBA
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UBC
Wed 5 Mar 2014, 3:00pm
Probability Seminar
ESB 2012
Hyperbolic random maps and unicellular maps
ESB 2012
Wed 5 Mar 2014, 3:00pm-4:00pm

Abstract

 Uniform infinite maps arise as local limits of uniformly chosen finite maps. Recently there has been keen interest in creating hyperbolic analogues of the uniform infinite planar maps. It is conjectured that uniformly distributed maps on surfaces with genus linear in the number of vertices should converge in the local topology to hyperbolic versions of uniform infinite maps. I will describe several models of such hyperbolic random maps which arise from several directions. Finally I will describe some recent results obtained for unicellular maps in high genus. Partly joint work with Omer Angel, Guillaume Chapuy and Nicolas Curien.
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University of Texas at Austin
Wed 5 Mar 2014, 3:15pm
Topology and related seminars
ESB 4133
Right-angled Artin subgroups of mapping class groups and Out(F)
ESB 4133
Wed 5 Mar 2014, 3:15pm-4:15pm

Abstract

There are many analogies between the outer automorphism group of a free group Out(F) and the mapping class group of a surface Mod(S). I'll explain how each of these groups contains many right-angled Artin subgroups and how these subgroups can be used to understand the structure of both Mod(S) and Out(F). Interestingly, attempting to understand the properties of elements in right-angled Artin subgroups also reveals some major differences between Out(F) and Mod(S). I'll explain these differences and how they affect the study of Out(F).
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Amir Maleki
Mech. Eng. Dep. UBC
Wed 5 Mar 2014, 4:00pm
Fluids Lab Meeting
LSK 203
MacroSize Drop Encapsulation
LSK 203
Wed 5 Mar 2014, 4:00pm-5:00pm

Abstract

Yield stress fluids have the property that they do not deform unless a given yield stress is exceeded. While in some flows this leads to unwanted features, this property can also be exploited in order to produce novel flow features. One example of such flows are visco-plastically lubricated (VPL) flows, in which a yield stress fluid is used to stabilize the interface in a multi-layer flow, far beyond what might be expected for a typical viscous-viscous interface. Here we extend this idea by considering the encapsulation of droplets within a visco-plastic fluid, for the purpose of transportation, e.g. in pipelines. The main advantage of this method, compared to others that involve capillary forces is that significantly larger droplets may be stably encapsulated, governed by the length scale of the flow and yield stress of the encapsulating fluid. We explore this setup both analytically and computationally. We show that sufficiently small droplets are held in the unyielded plug of the Poiseuille flow. As the length or radius of the droplets increase the carrier fluid eventually yields, potentially breaking the encapsulation. We study this process of breaking and give estimates for the limiting size of droplets that can be encapsulated.


Amir joined UBC for his master studies in the field of mechanical engineering in 2012. He is now working under supervision of Dr. Ian Frigaard in the complex fluids lab. He got his undergrad in 2011 from Sharif University of Technology.
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College of the Holy Cross
Thu 6 Mar 2014, 3:30pm
Number Theory Seminar
room ESB 4127 (PIMS-UBC)
Weyl group multiple Dirichlet series of type C_n
room ESB 4127 (PIMS-UBC)
Thu 6 Mar 2014, 3:30pm-4:30pm

Abstract

We construct Weyl group multiple Dirichlet series associated to root systems of type C, through a combinatorial recipe involving Gelfand-Tsetlin patterns. These Dirichlet series are associated with an n-fold metaplectic cover of SO(2r+1) and we prove functional equations for them when n=1, via the Casselman-Shalika formula. We also prove that our description matches the so called "stable case," as described for general root systems by Brubaker, Bump and Friedberg. This is joing work with Jennifer Beineke and Ben Brubaker.
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Daniel Valesin and Raimundo Briceno
UBC
Thu 6 Mar 2014, 4:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102
Phase Transitions and Computational Complexity (II)
Math Annex 1102
Thu 6 Mar 2014, 4:00pm-5:30pm
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UBC
Fri 7 Mar 2014, 3:00pm
Graduate Student Seminar
MATX 1100
What is... the Fundamental Group?
MATX 1100
Fri 7 Mar 2014, 3:00pm-4:30pm

Abstract

 I will talk about one of the simplest and most important functors of algebraic topology, the fundamental group, which gives an algebraic object obtained from the loops on a space.

Note for Attendees

 Pizza and pop will be provided.

Please note the special day and time.
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UBC
Fri 7 Mar 2014, 3:00pm
Graduate Student Seminar
MATX 1100
The Wonderful World of - - Disney- - Modular Forms.
MATX 1100
Fri 7 Mar 2014, 3:00pm-4:30pm

Abstract

In this talk, we will discuss modular forms, what they are and why they are amazing. Topics we will discuss include equalities of values of \sigma_{n} (sums of powers of divisors), the sum of four squares theorem, a discussion on Ramanujan's constant, an aside on polynomials with many prime terms, and perhaps even a bit of moonshine. Little will be completely proved but this talk will leave you in awe and wonder of this powerful concept.

Note for Attendees

Pizza and pop will be provided. 

Please note the special day and time.
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Department of Mathematics and Computer Science, Emory University
Mon 10 Mar 2014, 3:00pm SPECIAL
Institute of Applied Mathematics
LSK 460
Complex Networks for Mathematicians (IAM-PIMS Distinguished Colloquium)
LSK 460
Mon 10 Mar 2014, 3:00pm-4:00pm

Abstract

Network Science is a rapidly growing interdisciplinary area at  the intersection of mathematics, computer science, and a multitude of disciplines from the natural and life sciences to the social sciences and even the humanities.  Network analysis methods are now widely used in proteomics, in the study of social networks (both human and animal), in finance, in ecology, in bibliometric studies, in archeology, and in a host of other fields.
In this talk I will introduce the audience to some of the mathematical and computational problems and methods of complex networks, with an emphasis on the basic notions of centrality and communicability.  More specifically, I will describe some of the problems in large-scale numerical linear algebra arising in this area, and how they differ from the corresponding problems encountered in more traditional applications  of numerical analysis.
The talk will be accessible to students, requiring only a modest background in linear algebra and graph theory.

Note for Attendees

Refreshments start 15 minutes before the talk in the IAM Lounge, Room 306 of the LSK building.
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Wisconsin
Mon 10 Mar 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
The de Rham complex from the point of view of twisted derived intersections
ESB 4127 (host: UBC)
Mon 10 Mar 2014, 3:00pm-4:00pm

Abstract

I shall present results of work with Arinkin and Hablicsek which allow us to understand the Frobenius push-forward of the de Rham complex as the structure sheaf of a twisted derived intersection. Similar considerations also apply for twisted de Rham complexes, yielding results which have applications in singularity theory and in the study of matrix factorizations. Using our theorems we recover and strengthen earlier results of Deligne-Illusie, Barannikov-Kontsevich, and Sabbah. Our approach gives a new point of view on recent works of Joyce et al, generalizing results of Behrend, on understanding the holomorphic Fukaya-Floer homology.

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Philippe Castillon
Montpellier / PIMS-UBC
Tue 11 Mar 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Spectral positivity on surfaces
ESB 2012
Tue 11 Mar 2014, 3:30pm-4:30pm

Abstract

We shall see how the positivity of some Schr\"odinger operator on a surface gives information on its topology and its conformal type. The potent of the operators considered here involve the curvature of the surface and appear naturally in the study of minimal and constant mean curvature surfaces. It is a joint work with Pierre B\'erard.
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UAlberta
Wed 12 Mar 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
A Variation of the Beilinson-Hodge Conjecture
ESB 4127 (host: UAlberta)
Wed 12 Mar 2014, 3:00pm-4:00pm

Abstract

Based on some recent joint work of J. Lewis, and others, we formulate a variation of the Beilinson-Hodge conjecture pertaining to varieties defined over the complex numbers. In this talk, we explain the motivation for this conjecture, and some evidence in support of it. 
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University of Warwick
Wed 12 Mar 2014, 3:00pm
Probability Seminar
ESB 2012
Large deviations and gradient flow
ESB 2012
Wed 12 Mar 2014, 3:00pm-4:00pm

Abstract

We outline recent work uncovering intriguing connections between Otto's characterisation of diffusion as entropic gradient  flow on one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other. Specifically, we connect macroscopic gradient flows with large deviation principles, and point out the potential of a bigger picture emerging: we indicate that in some non-equilibrium situations, entropies and thermodynamic free energies can be derived via large deviation principles. The approach advocated in the talk  is different from the established hydrodynamic limit passage but extends a link that is well known in the equilibrium situation.
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Dr. Behzad Baghapour
Mech Eng Dept, University of Tehran
Wed 12 Mar 2014, 4:00pm
Fluids Lab Meeting
LSK 203
Discontinuous Galerkin Simulation of Compressible Flows on many-core GPUs
LSK 203
Wed 12 Mar 2014, 4:00pm-5:00pm

Abstract

The Discontinuous Galerkin (DG) method is very suitable for studying flows with mesh and accuracy adaptation due to weakly imposition of inter-element continuity. Moreover, DG provides sufficient stability for high-order finite-element schemes by direct implementation of flux upwinding.  Here a robust, high-order and fast DG solver was developed for compressible flows.  For increasing the accuracy, Hermitian super-parametric curved elements were designed for high-order boundary representation. For increasing the convergence rate, a Newton-Krylov algorithm was developed for pseudo-time advancement of the semi-discrete system. Local time-step adjustment based on flow history was introduced to stabilize the solution especially in startup iterations. To maximize the computational efficiency, the developed code was parallelized on the state-of-the-art Graphics Processing Unit (GPU) hardware with multiple layer of parallelism. According to compact nature of DG discretization, the fast block-tridiagonal solvers have been adapted recently both for structured and unstructured grids. A parallel Block Cyclic Reduction (BCR) linear solver was developed to work with DG on GPU. The developed solver has an improved speedup comparing with previous works due to optimizations in on-chip memory bandwidth and floating-point arithmetic rate. The proposed GPU-DG solver showed that it can be efficiently used in a wide range of high-order fluid flow simulations.   

Dr. Baghapour finished his PhD at University of Tehran in the field of mechanical engineering in 2014. He worked under the supervision of Dr. Vahid Esfahanian in Vehicle, Fuel and Environment Research Institute (VFERI). He also got his MSc degree under the supervision of Dr. Mehdi Ashjaee in Laser Diagnostic laboratory of University of Tehran. He is now a research assistant at Simon Fraser University working on hydrodynamics.
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Université Lille 1
Thu 13 Mar 2014, 3:30pm
Number Theory Seminar
room MATH 126
Prime numbers: emergence and relevance of bilinear forms decomposition
room MATH 126
Thu 13 Mar 2014, 3:30pm-4:30pm

Abstract

This talk will retrace the main steps of the modern theory of prime numbers and in particular how the combinatorial sieve combined with the Dirichlet series theory to give birth to the modern representation of the primes via a linear combination of terms, some of which being "linear", while the other ones are "bilinear". This will lead us to the recent developments of Green & Tao, Mauduit & Rivat, Tao, Helfgott, and Bourgain, Sarnak & Ziegler.
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Raimundo Briceno
UBC
Thu 13 Mar 2014, 4:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102
Phase Transitions and Computational Complexity (III)
Math Annex 1102
Thu 13 Mar 2014, 4:00pm-5:30pm
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University of Southern California
Thu 13 Mar 2014, 4:00pm
Algebraic Groups and Related Structures
Math Annex (MATX) 1118
Strongly Dense Subgroups of Semisimple Algebraic Groups
Math Annex (MATX) 1118
Thu 13 Mar 2014, 4:00pm-5:00pm

Abstract

Let G be a semisimple algebraic group over an algebraically closed field. A nonabelian free subgroup H is called strongly dense if every nonabelian subgroup of H is Zariski dense in G. We will discuss some recent results (with Breuillard, Green and Tao) regarding the existence of strongly dense subgroups and mention applications of these results to the Banach-Hausdorff-Tarski paradox, generation of finite simple groups of Lie type and the existence of families of expander graphs associated to finite groups of Lie type of fixed rank. If time permits, I will discuss some improvements with Breuillard and Larsen and the possibility of proving a generalizations of the Tits alternative.
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University of Southern California
Fri 14 Mar 2014, 3:00pm
Department Colloquium
ESB 2012 (PIMS)
Finite Simple Groups and Applications (PIMS/UBC Distinguished Colloquium)
ESB 2012 (PIMS)
Fri 14 Mar 2014, 3:00pm-4:00pm

Abstract

The classification of finite simple groups is of fundamental importance in mathematics.  It is also one of the longest and most complicated proofs in mathematics. We will very briefly discuss the result and a bit of history and then explain how it can and has been used to solve problems in many areas.  We will end with mentioning some specific and perhaps surprising consequences in various fields.

Note for Attendees

 Coffee, tea and cookies served at 2:30pm in the PIMS Lounge.
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Stanford
Mon 17 Mar 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Categorified Donaldson-Thomas invariants for sheaves
ESB 4127 (host: UBC)
Mon 17 Mar 2014, 3:00pm-4:00pm

Abstract

We will present a joint work with Young-Hoon Kiem on using family Chern-Simons charts to construct perverse sheaves on moduli of sheaves that gives a categorification of Donaldson-Thomas invariants.
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Mathematics Department, UBC
Mon 17 Mar 2014, 3:00pm
Institute of Applied Mathematics
LSK 460
Numerical simulations of proppant transport in hydraulic fractures induced by a slurry
LSK 460
Mon 17 Mar 2014, 3:00pm-4:00pm

Abstract

Hydraulic fracturing (HF) is a process where the material, such as rock, is cracked by a pressurized fluid. Among many applications of HF, the most common use is the stimulation of production from oil and gas wells. To prevent fracture from closing after the pressure is reduced, the propping agents, such as sand, are pumped together with the fracturing fluid. The problems of fluid-driven fracture propagation and flow of the suspensions have been studied extensively, but not many works combine both and address the fracturing caused by a slurry. To fill the gap, the aim of this study is to develop a computational model for calculating the propagation of a fracture induced by the viscous fluid mixed with the spherical particles. First, the empirical constitutive law for the slurry is used to obtain the solution for the steady flow of the viscous fluid mixed with spherical particles in a channel. This solution is then used to formulate the conservation laws for the slurry and the particles, which govern the propagation of hydraulic fractures and the proppant transport inside them. The developments are applied to two fracture geometries -- one-dimensional Khristianovich-Zheltov-Geertsma- De Klerk (KGD) and pseudo-3D (P3D). Numerical simulations show that the proposed method allows to capture the proppant plug (the region of compacted sand) formation and growth, as well as the gravitational settling for both geometries. Calculations with different proppant size demonstrate that bigger particles tend to settle faster, but, at the same time, promote fluid filtration through the plug, which supports further fracture propagation. Another problem that is addressed in this presentation is generation of proppant schedule. Certain proppant distribution inside the fracture is often desired at the end of pumping, however, only special proppant pumping schedule may lead to this. A new methodology of proppant schedule generation is introduced. It avoids solving an inverse problem and, at the same time, is more accurate than the commonly used procedure. One of the biggest advantages of the proposed approach is its compatibility with numerous HF simulators, making it a universal tool for generating a proppant schedule.
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Mary Beisiegel
Oregon State University
Tue 18 Mar 2014, 12:30pm SPECIAL
Lunch Series on Teaching & Learning
Math 126
A dip in the shallow end is not enough: Developing a deeper approach to cultivate mathematics graduate students’ teaching practices
Math 126
Tue 18 Mar 2014, 12:30pm-2:00pm

Abstract

The format of mathematics instruction in post-secondary contexts has remained problematic for undergraduate learners. Thus, the need to address the teaching practices of current and future teachers of post-secondary mathematics has become apparent. In preparing mathematics graduate students for their teaching responsibilities, many mathematics departments offer their new teaching assistants a one-time training session that addresses issues such as how to create quizzes, deal with disciplinary issues, and other practical matters. Beyond these shallow experiences, mathematics graduate students receive little support or mentorship for the development of their teaching practices. In this presentation, I will talk about three topics: my past research with mathematics graduate students, my current work on the creation of professional development experiences and support for mathematics graduate students, and my future work on the evolution of a deeper approach to cultivating mathematics graduate students’ teaching practices.

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Dominique Orban
GERAD and Ecole Polytechnique, Montreal
Tue 18 Mar 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133
The Projected Golub-Kahan Process for Constrained Linear Least-Squares Problems
ESB 4133
Tue 18 Mar 2014, 12:30pm-2:00pm

Abstract

A preconditioned variant of the Golub-Kahan bidiagonalization process recently proposed by Arioli and Orban allows us to establish that SYMMLQ and MINRES applied to least-squares problems in symmetric saddle-point form perform redundant work and are combinations of methods such as LSQR and LSMR. A well-chosen preconditioner allows us to formulate a projected variant of the Golub-Kahan process that forms the basis of specialized numerical methods for linear least-squares problems with linear equality constraints. As before, full-space methods such as SYMMLQ and MINRES applied to the symmetric saddle-point system defining the optimality conditions of such problems perform redundant work and are combinations of projected variants of LSQR and LSMR. We establish connections between numerical methods for least-squares problems, full-space methods and the projected and constraint-preconditioned Krylov methods of Gould, Orban and Rees.
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McGill University
Tue 18 Mar 2014, 4:00pm
Discrete Math Seminar
ESB 4133
Worst-case performance of online vector bin packing
ESB 4133
Tue 18 Mar 2014, 4:00pm-5:00pm

Abstract

In the d-dimensional bin packing problem (VBP), one is given vectors x1, x2, …, xn in Rd and the goal is to partition them into a minimum number of "feasible" sets. A set is feasible if the sum of its vectors does not have a component exceeding 1. Online VBP refers to the case where the vectors arrive sequentially and an algorithm must try to create these feasible sets on the fly. This problem has received renewed interest due to its relevance to placing virtual machines in a cloud platform.

The competitive ratio for an online algorithm is an upper bound on its worst case performance against an adversary which tries to choose a difficult sequence of incoming vectors. It had been outstanding for almost 20 years to clarify the gap between the best lower bound W(1) on the competitive ratio for online VBP versus the best upper bound of O(d). We settle this by describing a W (d / log d) lower bound. We also present several remaining open questions in the area.


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UBC
Wed 19 Mar 2014, 3:00pm
Probability Seminar
ESB 2012
Scaling limits and critical behaviour of the 4-dimensional n-component phi^4 spin model
ESB 2012
Wed 19 Mar 2014, 3:00pm-4:00pm

Abstract

The n-component phi^4 model is a ferromagnetic continuous-spin model with interesting critical behaviour.  In particular, the one-component model is predicted to be in the same universality class as the Ising model. We study the n-component model on the 4-dimensional integer lattice, for all n greater than or equal to 1, with small coupling constant.  We prove that the susceptibility has a logarithmic correction to mean field scaling, with exponent (n+2)/(n+8) for the logarithm.
 
We also analyse the asymptotic behaviour of the pressure as the critical point is approached, and prove that the specific heat hasfractional logarithmic scaling for n=1,2,3; double logarithmic scaling for n=4; and is bounded when n>4.  In addition, for the model defined on the 4-dimensional discrete torus, we prove that the scaling limit near the critical point is a multiple of the Gaussian free field on the continuum torus, whereas, in the subcritical regime, the scaling limit is Gaussian white noise with intensity equal to the susceptibility.
 
The proofs are based on a rigorous renormalisation group method.

This is joint work with Roland Bauerschmidt and David Brydges.
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UPenn
Wed 19 Mar 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
Towards Unifying Toric Mirror Constructions
ESB 4127 (host: UAlberta)
Wed 19 Mar 2014, 3:00pm-4:00pm

Abstract

I will discuss the recent work(-in-progress) on unifying various mirror constructions of various authors, such as Batyrev-Borisov and Berglund-Hübsch-Krawitz. This talk hopes to focus on questions, conjectures, and examples involved in this more generalized framework. This talk hopes not to focus on the difficulty of using a SmartBoard for seminars.
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University of Washington
Wed 19 Mar 2014, 3:15pm
Topology and related seminars
ESB 4133
Algebraic topology and algebraic torsors
ESB 4133
Wed 19 Mar 2014, 3:15pm-4:15pm

Abstract

I will discuss some types of problems where techniques from algebraic topology have led to successful resolutions of open problems in algebraic geometry. Then, I will outline several future directions where better knowledge of the topology of classifying spaces of compact Lie groups could lead to more results in algebra.
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CS UBC
Thu 20 Mar 2014, 12:30pm
Graduate Student Seminar
Math 204
Application of two-dimensional cell complexes to vector graphics
Math 204
Thu 20 Mar 2014, 12:30pm-2:00pm

Abstract

Vector graphics software, such as Adobe Illustrator or Inkscape, typically use a data-structure made of paths independent from each other. This makes representing incidence relationships difficult.

With Rémi Ronfard and Michiel van de Panne, we developed a more topology-oriented data-structure, made of vertices, edges and faces, that I will first present. Then I will show how this combinatorial structure is in fact a presentation scheme whose geometric realization is (to the best of our computer scientist knowledge) a new kind of two-dimensional "cell" complex, that we call Point-Curve-Surface complex (PCS complex). We are currently trying to prove that every two-dimensional simplicial complex has a unique minimal PCS complex decomposition.

Note for Attendees

Pizza and pop will be provided.


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Myrto Mavraki
Mathematics, UBC
Thu 20 Mar 2014, 12:30pm
Graduate Student Seminar
Math 204
Arithmetic Dynamics
Math 204
Thu 20 Mar 2014, 12:30pm-2:00pm

Abstract

This short talk will focus on the interplay between number theory and dynamical systems by briefly describing some interesting yet simple to state questions.

Note for Attendees

 Pizza and pop will be provided.
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UCLA
Thu 20 Mar 2014, 3:30pm
Number Theory Seminar
room MATH 126
On the non-triviality of Heegner points modulo p
room MATH 126
Thu 20 Mar 2014, 3:30pm-4:30pm

Abstract

Let l and p be distinct odd primes unramified in an imaginary quadratic extension K/Q. We outline the proof of the non-triviality of the p-adic formal group logarithm of Heegner points modulo p associated to the Rankin-Selberg convolution of an elliptic modular form of weight two and a theta series over the Zl-anticyclotomic extension of K. We also make remarks regarding the analogous non-triviality of generalised Heegner cycles.
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Raimundo Briceno
UBC
Thu 20 Mar 2014, 4:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102
Phase transitions and computational complexity (IV)
Math Annex 1102
Thu 20 Mar 2014, 4:00pm-5:30pm
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University of Oregon
Fri 21 Mar 2014, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (PIMS building) note the time and location change
Complex Monge-Ampere equation on Kahler manifolds
ESB 2012 (PIMS building) note the time and location change
Fri 21 Mar 2014, 3:30pm-4:30pm

Abstract

Complex Monge-Ampere (CMA) equation is of fundamental importance in Kahler geometry. We will discuss regularity results for two versions of complex Monge-Ampere equation which are extensively studied in Kahler geometry. The first is the classical CMA equation solved by S.T. Yau in 1970s to prove the Calabi conjecture. The second  is a homogenous complex Monge-Ampere, which is known as a geodesic equation of the space of Kahler metrics.
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Ohio State University
Mon 24 Mar 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Curves on Irreducible Holomorphic Symplectic Varieties
ESB 4127 (host: UBC)
Mon 24 Mar 2014, 3:00pm-4:00pm

Abstract

The goal of the talk is to present derived category techniques to study holomorphic symplectic varieties. In particular, we study and answer the following questions:

(1) the Hassett-Tschinkel Conjecture on the structure of the Mori cone of curves;
(2) the Bogomolov-Tyurin-Hassett-Tschinkel-Huybrechts-Sawon Conjecture on the existence of Lagrangian fibrations;
(3) the Kawamata-Morrison Cone Conjecture.

Irreducible Holomorphic Symplectic varieties (IHS for short) are simply connected projective manifolds endowed with a unique (up to scalars) holomorphic symplectic form; K3 surfaces are the lowest dimensional example. In this talk we concentrate on IHS of K3^[n]-type, namely IHS deformation equivalent to the punctual Hilbert scheme on a K3 surface. After giving a short introduction to the basics of IHS theory, we will present recent joint work with Arend Bayer on how to prove (1), (2), and (3) for moduli spaces of sheaves on K3 surfaces, by using derived categories and Bridgeland stability. If time permits, I will also sketch how to extend these results to all IHS of K3^[n]-type, as recently proven by Bayer-Hassett-Tschinkel, Mongardi, Matsushita, Markman-Yoshioka, and Amerik-Verbitsky.
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Mathematics, UBC
Mon 24 Mar 2014, 3:00pm
Institute of Applied Mathematics
LSK 460
Logarithmic Expansions and the Stability of Periodic Patterns of Localize d Spots for Reaction-Diffusion Systems in Two Dimensions
LSK 460
Mon 24 Mar 2014, 3:00pm-4:00pm

Abstract

We determine the stability threshold for a periodic arrangment of localized spots for some singularly perturbed two-component reaction-diffusion systems including the Gierer-Meihardt, Schnakenburg, and Gray-Scott models, in R^2. In the semi-strong interaction asymptotic limit where only one of the components has an asymptotically small diffusivity, the leading order stability threshold governing amplitude instabilities of the spots, as derived by Wei-Winter (2001, 2003), is independent of the arrangement of the spots in the lattice. By combining a spectral approach based on Floquet-Bloch theory together with the method of matched asymptotic expansions and appropriate Fredholm solvability conditions, we calculate the next order term in the expansion of the stability threshold in terms of the regular parts of certain Green's functions. In this way, we derive an asymptotic result for the location of a real-valued band of continuous spectrum for the linearized operator when a stability parameter is close to its critical value. This result depends on an objective function defined in terms of both the Bloch wavevector and the particular lattice arrangment. From a numerical min-max optimization of this objective function it is shown that a regular hexagonal lattice of localized spots is the most stable. Joint work with Juncheng Wei (UBC), David Iron (Dalhousie) and John Rumsey (Dalhousie)
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Warwick
Tue 25 Mar 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133
Accelerating the Dimer Algorithm for Computing Saddle Points
ESB 4133
Tue 25 Mar 2014, 12:30pm-2:00pm

Abstract

The dimer method is a simple hessian-free algorithm for computing index-1 saddles. In this talk, I will review and analyze a few variants of this algorithm, focusing on some improvements to its efficiency, in particular adding preconditioning capabilities and line-search based on a local merit function. I will demonstrate the efficiency of the new variant on a range of applications from academic toy problems, an atomistic problem and a PDE problem.

Despite these new improvements, we can currently give no global convergence guarantee. Indeed, we can construct counterexamples to global convergence. I will conclude my talk by explaining some of the difficulties we encountered.

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Christian Sadel
UBC
Tue 25 Mar 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Complex analytic, one-frequency cocycles
ESB 2012
Tue 25 Mar 2014, 3:30pm-4:30pm

Abstract

 
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Rami Tabbara
University of Melbourne
Tue 25 Mar 2014, 4:00pm
Discrete Math Seminar
ESB 4133
Counting two interacting friendly walks near an attractive surface
ESB 4133
Tue 25 Mar 2014, 4:00pm-5:00pm

Abstract

We will describe a class of two directed and friendly walks along the
square lattice that are restricted to the upper half-plane. One
motivation for studying this class is that it can be used to model an
idealised thermodynamic system of a DNA strand in a solvent near an
attractive surface. We will solve the combinatorial problem of finding
a closed-form expression for the number of $N$ paired walks that
contain $L$ lower-walk-to-$x$-axis and $M$ lower-walk-to-upper-walk
shared site contacts.
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UBC
Wed 26 Mar 2014, 3:15pm
Topology and related seminars
ESB 4133
A Classifying Space for Commutativity for Lie Groups
ESB 4133
Wed 26 Mar 2014, 3:15pm-4:15pm

Abstract

In this talk we will define a space built out of all the commuting n-tuples in a Lie group and discuss its role as a classifying space for commutativity.  Applied to the unitary groups this gives rise to an infinite loop space and the notion of commutative K-theory. We will also provide computations for the rational cohomology in terms of mult-symmetric invariants. This is joint work with Jose Gomez.

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Yuichi Hirano
University of Tokyo
Thu 27 Mar 2014, 3:30pm
Number Theory Seminar
room MATH 126
Congruences of Hilbert modular forms over real quadratic fields and the special values of L-functions
room MATH 126
Thu 27 Mar 2014, 3:30pm-4:30pm

Abstract

Let F be a totally real number field. We consider the problem to show how congruences between the Fourier coefficients of a Hilbert eigenform over F and a Hilbert Eisenstein series over F (of the same parallel weight (k,...,k)) give rise to corresponding congruences between the algebraic parts of the special values of the associated L-functions. In the case Q, the congruences of L-functions were obtained by Vatsal (k=2), Heumann--Vatsal (k≥2), and the speaker (k≥2). In this talk, we generalize Vatsal's work to the case F is a real quadratic field and k=2.
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Raimundo Briceno
UBC
Thu 27 Mar 2014, 4:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102
Phase transitions and computational complexity (V)
Math Annex 1102
Thu 27 Mar 2014, 4:00pm-5:30pm
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UC Santa Barbara
Fri 28 Mar 2014, 3:00pm
Department Colloquium
ESB 2012 (PIMS)
The Emerging Roles and Computational Challenges of Stochasticity in Biological Systems (PIMS/UBC Distinguished Colloquium)
ESB 2012 (PIMS)
Fri 28 Mar 2014, 3:00pm-4:00pm

Abstract

 In recent years it has become increasingly clear that stochasticity plays an important role in many biological processes.  Examples include bistable genetic switches, noise enhanced robustness of oscillations, and fluctuation enhanced sensitivity or “stochastic focusing"..  Numerous cellular systems rely on spatial stochastic noise for robust performance.   We examine the need for stochastic models, report on the state of the art of algorithms and software for modeling and simulation of stochastic biochemical systems, and identify some computational challenges.

Note for Attendees

 Coffee, tea and cookies served at 2:30pm in the PIMS Lounge.
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