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 Events
UBC
Mon 3 Oct 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Derived Moduli of Noncommutative Projective Schemes
WMAX 110
Mon 3 Oct 2011, 3:10pm-4:10pm

Abstract

I will talk on joint work in progress with Behrang Noohi.  We study the GIT problem given by the differential graded Lie algebra of Hochschild cochains of a finite graded algebra.  This will lead to a definition of stability for non-commutative polarized projective schemes, and to the construction of quasi-projective moduli spaces for them.  These moduli spaces are differential graded schemes. There may be new moduli spaces with symmetric obstruction theories coming out of this.
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Izabella Laba
UBC
Mon 3 Oct 2011, 4:00pm
Harmonic Analysis Seminar
MATX 1102
Buffon's needle probability for rational product Cantor sets, part 2
MATX 1102
Mon 3 Oct 2011, 4:00pm-5:00pm

Abstract

This talk is a continuation of Matt Bond's talk from Sept 19: We investigate the probability that "Buffon's Needle" lands near a one-dimensional self-similar product set in the complex plane, where the similarity maps have rational centers and identical scalings. If the factors A and B are defined by at most 6 similarities, then the likelihood that the needle intersects an e^{-n}-neighborhood of such a set is at most Cn^{-p/\log\log n} for some p>0. (Joint work with M. Bond and A. Volberg.)
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Costanza Piccolo
UBC
Tue 4 Oct 2011, 12:30pm SPECIAL
One Time Event
MATX 1102
Lunch Series for Teaching and Learning: The Course Archive Project, a Teaching Resource for Everyone
MATX 1102
Tue 4 Oct 2011, 12:30pm-1:30pm

Details

Are you teaching a course for the first time and would like to see old midterm exams? Are you looking for old course materials from when you taught the same course a few years ago but can't find them? Would you like to have access to old homework assignments and worked solutions for the course you are teaching? Have you ever had to spend time collecting and compressing files to share course materials with your colleagues only to find out that your zip file is too big to send by email?

If any of these applies to you, then the Course Archive Project (CAP) is what you need. Now available on a secure department site, CAP allows you to store, search through, and easily access commonly-used course materials. We will give a short demo of the site and discuss effective ways to organize materials, including strategies to upload documents and enter information. Pizza and pops will be available.

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Will Thompson
UBC
Tue 4 Oct 2011, 2:00pm
Stochastic Dynamics Working Group
IAM Lounge (LSK 306)
Noise driven synchronization of two conditional oscillators
IAM Lounge (LSK 306)
Tue 4 Oct 2011, 2:00pm-3:00pm

Abstract


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David Kohler
UBC
Tue 4 Oct 2011, 2:00pm
Mathematical Education
MATX 1101
How to Prepare To Teach ?
MATX 1101
Tue 4 Oct 2011, 2:00pm-3:00pm

Abstract

We'll present and discuss the third chapter of Ken Bain's "What Best College Teachers Do". More detail under : wiki.ubc.ca/Sandbox:MathTeachingSeminar
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UBC
Tue 4 Oct 2011, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (PIMS)
Regularity for the optimal transport problem with Euclidean distance squared cost on the embedded sphere
WMAX 110 (PIMS)
Tue 4 Oct 2011, 3:30pm-4:30pm

Abstract

We consider regularity for Monge solutions to the optimal transport problem when the initial and target measures are supported on the embedded sphere, and the cost function is the Euclidean distance squared. Gangbo and McCann have shown that when the initial and target measures are supported on boundaries of strictly convex domains in $\mathbb{R}^n$, there is a unique Kantorovich solution, but it can fail to be a Monge solution. By using PDE methods, in the case when we are dealing with the sphere with measures absolutely continuous with respect to surface measure, we present a condition on the densities of the measures to ensure that the solution given by Gangbo and McCann is indeed a Monge solution, and obtain higher regularity as well. This talk is based on joint work with Micah Warren.
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UBC
Tue 4 Oct 2011, 3:30pm
Algebraic Groups and Related Structures
MATX 1101
Galois Cohomology associated to Central Simple Algebras with Involution
MATX 1101
Tue 4 Oct 2011, 3:30pm-4:30pm

Abstract

 We present some of the Galois Cohomology set associated to central simple algebras with involutions.
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Gyula Karolyi
Eotvos University
Tue 4 Oct 2011, 4:00pm
Discrete Math Seminar
Matx 1102
Constant term identities for Laurent polynomials
Matx 1102
Tue 4 Oct 2011, 4:00pm-5:00pm

Abstract

The computation of the joint probability distribution
of the eigenvalues of random matrices originating in
statistical mechanics often leads to the evaluation
of a Selberg-type integral which can be reduced to a
problem in algebraic combinatorics. Such a problem
was first identified by Dyson in 1962, leading to
far reaching generalizations. We present a simple
algebraic method which among others leads to a very
short proof of Andrews' q-Dyson conjecture as well as
to the solution of a long-standing open problem of
Forrester. 
 
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Giovanni Ghigliotti
UBC
Wed 5 Oct 2011, 2:00pm
Complex Fluids Seminar
Math Annex 1118
Vesicles and red blood cell clusters in Poiseuille flow
Math Annex 1118
Wed 5 Oct 2011, 2:00pm-3:00pm
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Prof. Masao Hara
Tokai University, Japan
Wed 5 Oct 2011, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)
Minimal crossing diagram and Jones polynomial
WMAX 216 (PIMS)
Wed 5 Oct 2011, 3:00pm-4:30pm

Abstract

It seemed quite difficult to determined crossing number of a link until Jones discovered a new polynomial invariant. Important results about crossing number of a link were shown after Kauffman gave a method for calculating Jones polynomial.

I will survey the relation between the reduced degree of Jones polynomial of a link and its crossing number and discuss Jones polynomial of a pretzel link. I will introduce an adequate diagram and discuss minimality of a diagram from the viewpoint of it. I will discuss the difference between the reduced degrees of Jones polynomials of pretzel links and their crossing numbers, and whether Jones polynomial is a complete invariant on alternating pretzel knots.
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Microsoft Research
Wed 5 Oct 2011, 3:00pm
Probability Seminar
MATH 126
Detection by Poisson Brownian motions
MATH 126
Wed 5 Oct 2011, 3:00pm-4:00pm

Abstract

Consider a Poisson point process of intensity \lambda in R^d and let each point move as an independent Brownian motion. Consider a target particle that is initially placed at the origin at time 0 and can move according to any continuous function. We say that the target is detected at time t if there exists at least one point of the point process within distance 1 of the target at time t. We show that if \lambda is sufficiently large, then the target will eventually be detected even if its motion can depend on the past, present and future positions of the points. In the proof we use coupling and multi-scale analysis to show that some good events percolate in space and time.
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Bernhard Konrad and Robert Klinzmann
UBC
Thu 6 Oct 2011, 12:30pm
Graduate Student Seminar
LSK 460
Graduate Student Colloquium
LSK 460
Thu 6 Oct 2011, 12:30pm-2:00pm

Abstract


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UBC
Thu 6 Oct 2011, 3:00pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
Roots of unity, torsion on fibers, and preperiodic points for families of rational maps
Room WMAX 216 (PIMS - UBC Campus)
Thu 6 Oct 2011, 3:00pm-3:50pm

Abstract

In early 1960's, Lang proved that if for a given polynomial G(X,Y) with complex coefficients, there exist infinitely many pairs (x,y) where both x and y are roots of unity such that G(x,y) = 0, then essentially G(X,Y) = X^mY^n - c, for some integers m and n, and a root of unity c. In 2009, Masser and Zannier proved a result (similar in the spirit of Lang's result) for torsion points on a family of elliptic curves. In our talk we explain how both results come from the same general principle in arithmetic geometry, and at the same time we present a partial result to a more general conjecture which subsumes both Lang and Masser-Zannier theorems.

Note for Attendees

Refreshments will be served between the two talks.
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UBC
Thu 6 Oct 2011, 4:10pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
Galois representations and deformations
Room WMAX 216 (PIMS - UBC Campus)
Thu 6 Oct 2011, 4:10pm-5:00pm

Abstract

Representations of the Galois group of the rationals abound in nature and are important in understanding the structure of the Galois group of the rational numbers. Iwasawa theory studies certain arithmetic modules arising from such representations. Hida theory provides a technique to package some of these representations in a family and study them simultaneously. In this talk I will demonstrate the usefulness of this technique in obtaining information on certain fundamental invariants arising in Iwasawa theory for such families and studying their variation within a family.
 
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UBC
Fri 7 Oct 2011, 3:00pm
Department Colloquium
MATX 1100
Scattering and blow-up of Schroedinger maps.
MATX 1100
Fri 7 Oct 2011, 3:00pm-4:00pm

Abstract

The Schroedinger map PDE is a simple, natural, geometric (hence nonlinear) generalization of the classical (linear) Schroedinger equation of quantum mechanics. Remarkably, it is also a basic model in ferromagnetism.

Without assuming a PDE background, I will discuss the key questions one asks about the qualitative properties of solutions of such equations -- which concern singularity (non)-formation and asymptotic behaviour -- leading up to results of mine (joint with Eva Koo, and with Kenji Nakanishi and Tai-Peng Tsai) and others which address these questions, and along the way touching on recent developments in the field of nonlinear dispersive equations more generally.
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Frank DeZeeuw
Fri 7 Oct 2011, 4:00pm SPECIAL
One Time Event
Graduate Student Center, Room 200
Doctoral Exam
Graduate Student Center, Room 200
Fri 7 Oct 2011, 4:00pm-7:00pm

Details

An algebraic view of discrete geometry

This thesis includes three papers and one expository chapter as background for one of the papers. They have in common that they combine algebra with discrete geometry, mostly by using algebraic tools to prove statements from discrete geometry. Algebraic curves and number theory also recur throughout the proofs and results.
In the first paper, we prove that an infinite set of points in the real plane such that all pairwise distances are rational cannot be contained in an algebraic curve, except if that curve is a line or a circle, in which case at most 4 resp. 3 points of the set can be outside the line or circle. In the proof we use the classi cation of curves by their genus, and Faltings' Theorem.
In the second paper, we prove a bound on the number of unit distances that can occur between points of a finite set in the real plane, under the restriction that the line segments corresponding to these distances make a rational angle with the horizontal axis. In the proof we use graph theory and an algebraic theorem of Mann.
In third paper, we give an upper bound on the length of a simultaneous arithmetic progression (a two-dimensional generalization of an arithmetic progression) on an elliptic curve, as well as for more general curves. We give a simple proof using a theorem of Jarnik, and another proof using the Crossing Inequality and some bounds from elementary algebraic geometry, which gives better explicit bounds.

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Mathematics Department, University of Toronto
Tue 11 Oct 2011, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 110
Inverse Problems with (Minimal) Interior Measurements
WMAX 110
Tue 11 Oct 2011, 12:30pm-1:30pm

Abstract

A new class of Inverse Problems seeks to significantly improve both the quantitative accuracy and the resolution of traditional inverse boundary value problems by using data which can be determined in the interior of the object. I will briefly explain how such measurements of current density can be obtained
using Magnetic Resonance Imaging in a non-standard way. Imaging electric conductivity then leads to beautiful mathematics involving minimal surfaces in a conformal metric determined by the measured data, and a corresponding variable coefficient least gradient problem.
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UBC
Tue 11 Oct 2011, 2:00pm
Stochastic Dynamics Working Group
IAM Lounge (LSK 306)
Noise-induced coherence and network oscillations in a reduced bursting model
IAM Lounge (LSK 306)
Tue 11 Oct 2011, 2:00pm-3:00pm

Abstract


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George Bluman
UBC
Tue 11 Oct 2011, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Some recent developments in symmetries and conservation laws for PDEs. Part I
Math Annex 1118
Tue 11 Oct 2011, 2:30pm-3:30pm

Abstract

This series of lectures will be concerned with some recent developments on how to find and use symmetries for PDEs; how to find and use conservation laws for PDEs; connections between symmetries and conservation laws for PDEs. Much of the material appears in Applications of Symmetry Methods to Partial Differential Equations (Bluman/Cheviakov/Anco), Springer (2010). Background material appears in Symmetry and Integration Methods for Differential Equations (Bluman/Cheviakov), Springer (2002) on Lie groups of transformations and their applications to solving ODEs, the construction of conservation laws (integrating factors) for ODEs, and finding invariant solutions of PDEs.  Both of these books are available online through the UBC library.

 

No background beyond undergraduate mathematics is necessary as a prerequisite for this series. These lectures were presented at Moscow State University in June 2011 and will flow as follows.

 

  1. General introduction giving an extensive overview of topics to be covered.
  2. Review of Lie’s work on point symmetries and invariant solutions for PDEs.
  3. Local symmetries—point, contact, higher-order.  How to find them for a given PDE system.
  4. Construction of conservation laws—direct method to find them, connections with Noether’s theorem.
  5. Use of symmetries to construct new conservation laws from known CLs.
  6. Invertible mappings of nonlinear PDEs to linear PDEs through symmetry analysis and through conservation law multiplier analysis.
  7. Invertible mappings of linear PDEs with variable coefficients to linear PDEs with constant coefficients.
  8. The nonclassical method to find solutions of PDEs.
  9. How to systematically find trees of equivalent but nonlocally related PDE systems for a given PDE system. 
  10. How to systematically find nonlocal symmetries and nonlocal conservation laws for a given PDE system.
  11. The multidimensional situation--gauge constraints.
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Cornell University
Tue 11 Oct 2011, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (PIMS)
Harnack Inequalities, Heat Kernel Estimates and the Ricci flow
WMAX 110 (PIMS)
Tue 11 Oct 2011, 3:30pm-4:30pm

Abstract

In this talk, we will discuss about Li-Yau-Hamilton type differential Harnack inequalities, heat kernel estimates and their applications to study type I ancient solutions of the Ricci flow. Some of this is joint work with Q. S. Zhang.
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UBC
Tue 11 Oct 2011, 4:00pm
Algebraic Groups and Related Structures
Math 126
A Derived Equivalence for some Projective Homogeneous Varieties
Math 126
Tue 11 Oct 2011, 4:00pm-5:00pm

Abstract

 We produce a derived equivalence for some examples of Projective Homogeneous Varieties (Severi-Brauer Varieties, Quadrics, and Involution Varieties) by constructing a Tilting Bundle in each case.
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Caleb Cheek
UBC
Tue 11 Oct 2011, 4:00pm
Discrete Math Seminar
Matx 1102
Decoding binary linear codes through linear programming
Matx 1102
Tue 11 Oct 2011, 4:00pm-5:00am

Abstract

A fairly recent thesis by John Feldman (MIT 2002) presents
maximum-likelihood decoding of binary linear codes as an integer
linear program. For LDPC and turbo-like codes, certain relaxations
allow for a good decoding algorithm. Since then, there have been a
number of results on improved versions of the LP decoder, suggesting
that it may become a more useful paradigm than more commonly used
message-passing algorithms.

Following a 2008 by Navin Kashyap (Queen's), we discuss an old but
previously neglected connection between codes and matroids. We give a
survey of results obtained by matroid decomposition techniques, and
their implications for LP decoding.

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University of Michigan
Wed 12 Oct 2011, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)
Bounds on eigenvalues of the Laplacian for certain hyperbolic 3-manifolds
WMAX 216 (PIMS)
Wed 12 Oct 2011, 3:00pm-4:00pm

Abstract

In this talk I will prove that in the presence of bounds for the rank of the fundamental group and the injectivity radius, the kth eigenvalue of the Laplacian of a closed hyperbolic 3-manifold M is bounded from above and below by a multiple of vol(M)^{-2}.
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ENS Paris
Wed 12 Oct 2011, 3:00pm
Probability Seminar
MATH 126
Strong convergence of partial match queries in random quadtrees
MATH 126
Wed 12 Oct 2011, 3:00pm-4:00pm

Abstract


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UBC
Fri 14 Oct 2011, 3:00pm
Department Colloquium
MATX 1100
Stochastic dynamics and HIV infection
MATX 1100
Fri 14 Oct 2011, 3:00pm-4:00pm

Abstract

I will present recent work on modelling treated HIV infection using branching process models.  We use simulations and novel numerical methods to calculate probability distribution functions for virus and cell concentrations. An overview of relevant HIV biology will be included in the talk. Most of this work is joint with Jessica Conway (UBC).
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UC Berkeley
Mon 17 Oct 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Twisted strong Macdonald theorems
WMAX 110
Mon 17 Oct 2011, 3:10pm-4:10pm

Abstract

Let L be a reductive Lie algebra. The strong Macdonald theorems of Fishel, Grojnowski, and Teleman state that the cohomology algebras of L[z]/z^N and L[z,s] (where s is an odd variable) are free skew-commutative algebras with generators in certain degrees. The theorems were originally conjectured by Hanlon and Feigin as Lie algebra cohomology extensions of Macdonald's constant term identity in algebraic combinatorics. The proof uses ideas from the Kahler geometry of the loop Grassmannian.

I will explain how to extend Fishel, Grojnowski, and Teleman's ideas to generalized flag varieties of (twisted) loop groups, and consequently get strong Macdonald theorems for p[s] and p/z^N p when p is a parahoric. When p has a non-trivial parabolic component the cohomology of p/z^N p is no longer free, as it contains a factor which is isomorphic to the cohomology algebra of the flag variety of the corresponding parabolic.
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Karlsruhe Institute of Technology, Germany
Tue 18 Oct 2011, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 110
A Fully Automatic hp-Adaptive Refinement Strategy
WMAX 110
Tue 18 Oct 2011, 12:30pm-1:30pm

Abstract

The finite element method is a widely accepted tool for the numerical solution of partial differential equations. Nowadays a posteriori error estimation is an expected and assessed feature in scientific computing. It is used for adaptively creating approximation spaces and to assess the accuracy of numerical solutions. The performance of the method can be improved by mesh refinement (h-refinement) or the use of higher oder ansatz spaces (p-refinement). Taking a combination of both (hp-refinement) can lead to exponentially fast convergence with respect to the number of degrees of freedom. Especially for hp-FEM there have been proposed several strategies for adaptively creating problem-dependent meshes, e.g. estimating the analyticity of the solution, solving local boundary value problems and minimize the global interpolation error can be minimized.

In this talk we present a fully automatic hp-adaptive refinement strategy, which is based on the solution of local boundary value problems. We present the strategy for the Poisson and the Maxwell boundary value problem and show convergence of the algorithm. The talk is concluded by some numerical examples.
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UBC
Tue 18 Oct 2011, 2:00pm
Mathematical Education
MATX 1101
What to Expect from the Students ?
MATX 1101
Tue 18 Oct 2011, 2:00pm-3:00pm

Abstract

In this talk, we present the 4th chapter of Bain's book. The problematic is to determine what college teachers should expect from their students. More info under : wiki.ubc.ca/Sandbox:MathTeachingSeminar
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UBC
Tue 18 Oct 2011, 2:00pm
Stochastic Dynamics Working Group
IAM Lounge (LSK 306)
Noise-induced coherence and network oscillations in a reduced bursting model (continued).
IAM Lounge (LSK 306)
Tue 18 Oct 2011, 2:00pm-3:00pm

Abstract


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George Bluman
UBC
Tue 18 Oct 2011, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Some recent developments in symmetries and conservation laws for PDEs. Part II: Local symmetries
Math Annex 1118
Tue 18 Oct 2011, 2:30pm-3:30pm

Abstract

In the second part of this series, we will consider the following topics.

1. Review of Lie’s work on point symmetries and the construction of invariant solutions for PDEs.

2.Local symmetries—point, contact, higher-order.  How to find them for a given PDE system.

 

It is not necessary to have attended the first part last week to follow along.

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UBC
Tue 18 Oct 2011, 3:00pm
One Time Event
MATH 103
TAAP Seminar: Effective Tutoring
MATH 103
Tue 18 Oct 2011, 3:00pm-4:00pm

Details

Tutoring is one of the most common TA assignments for new graduate students, and is a skill all TAs can benefit from improving.  But what makes a tutor effective?  What are some good practices to use while tutoring, and do we follow them?  In this session, we will examine questions such as these in a reflective process and discussion in an attempt to better our abilities as tutors.

This is the first talk in the TA Accreditation Program Seminar Series; more information can be found at

http://www.math.ubc.ca/~fsl/TAAP%20Seminar%20Series.html
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UBC
Tue 18 Oct 2011, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (PIMS)
Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system
WMAX 110 (PIMS)
Tue 18 Oct 2011, 3:30pm-4:30pm

Abstract

The relativistic Vlasov-Darwin (RVD) system is a kinetic model that describes the evolution of a collisionless plasma whose particles interact through the self-induced electromagnetic field. In contrast with the Vlasov-Maxwell system, the particle interaction is assumed to be a low-order relativistic correction (i.e., the Darwin approximation) to the full Maxwell case. A consequence of this assumption is that instead of the less tractable hyperbolic Maxwell equations, the resulting system has elliptic features even though there is a fully coupled magnetic field. We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the RVD system. Our proof extends the method used by Loeper in [J. Math. Pures Appl., 86 (2006), pp. 68-79 ] to obtain uniqueness results for the Vlasov-Poisson system. This is a joint work with Martial Agueh.
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Institut de Mathematiques de Jussieu
Tue 18 Oct 2011, 4:00pm
Algebraic Groups and Related Structures
Math 126
SK_1 and SK_2 of central simple algebras
Math 126
Tue 18 Oct 2011, 4:00pm-5:00pm

Abstract

 We discuss several constructions of homomorphisms from SK1 and SK2 of central simple algebras to subquotients of Galois cohomology groups.
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Mohammad Taghavi
Wed 19 Oct 2011, 2:00pm
Complex Fluids Seminar
MATX 1118
From Displacement to Mixing in a Slightly Inclined Duct
MATX 1118
Wed 19 Oct 2011, 2:00pm-3:00pm

Abstract

This work studies buoyant displacement flows with two miscible fluids in pipes and 2D channels that are inclined at angles close to horizontal. Detailed experimental, analytical and computational approaches are employed in an integrated fashion. The displacements are at low Atwood numbers and high Peclet numbers, so that miscibility effects are mostly observable after instability and via dispersive mixing. For iso-viscous Newtonian displacements, studying the front velocity variation as a function of the imposed flow velocity allows us to identify 3 distinct flow regimes: an exchange flow dominated regime characterized by Kelvin-Helmholtz-like instabilities, a laminarised viscous displacement regime with the front velocity linearly increasing with the mean imposed flow rate, and a fully mixed displacement regime. The transition between the first and the second regimes is found to be marked by a stationary layer of displaced fluid. In the stationary layer the displaced fluid moves in counter-current motion with zero net volumetric flux. Different lubrication/thin-film models have been used to predict the flow behaviour. We also succeed in characterising displacements as viscous or inertial, according to the absence/presence of interfacial instability and mixing. This dual characterisation allows us to define 5-6 distinct flow regimes, which we show collapse onto regions in a two-dimensional parameter plane. In each regime we have been able to offer a leading order approximation to the leading front velocity. A weighted residual method has also been used to include the effect of inertia within the lubrication modelling approach, which allows us to predict long-wave instabilities.

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UBC
Wed 19 Oct 2011, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)
Abstract Commensurators of the Johnson Filtration
WMAX 216 (PIMS)
Wed 19 Oct 2011, 3:00pm-4:00pm

Abstract

The Torelli group is the subgroup of the mapping class group which acts trivially on the homology of the surface. It is the first term of the Johnson filtration, the sequence of subgroups which act trivially on the surface group modulo some term of its lower central series. We prove that the abstract commensurator of each of these subgroups is the full mapping class group. This is joint work with Martin Bridson and Juan Souto.
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UBC
Wed 19 Oct 2011, 3:00pm
Probability Seminar
MATH 126
Non-uniqueness for parabolic stochastic PDE
MATH 126
Wed 19 Oct 2011, 3:00pm-4:00pm

Abstract


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Eugene Barsky (UBC Library) and Simon Rose
UBC
Thu 20 Oct 2011, 12:30pm
Graduate Student Seminar
LSK 460
Graduate Student Colloquium
LSK 460
Thu 20 Oct 2011, 12:30pm-2:00pm

Abstract


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UBC
Thu 20 Oct 2011, 3:00pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
The iterated Carmichael lambda function
Room ASB 10900 (IRMACS - SFU Campus)
Thu 20 Oct 2011, 3:00pm-3:50pm

Abstract

The Carmichael lambda function \lambda(n) is defined to be the smallest positive integer m such that a^m \equiv 1 \pmod{n} for all (a,n)=1. \lambda_k(n) is defined to be the k th iterate of \lambda(n). We will discuss some previous known results about k=1,2 as well as sketch a proof of a normal order for n/\lambda_k(n) for all k.

Note for Attendees

Refreshments will be served between the two talks.
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UBC
Thu 20 Oct 2011, 4:10pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
The generalized Fermat equation
Room ASB 10900 (IRMACS - SFU Campus)
Thu 20 Oct 2011, 4:10pm-5:00pm

Abstract

We will survey results on, and techniques for, the generalized Fermat equation x^p + y^q = z^r, where p, q, and r satisfy 1/p + 1/q + 1/r < 1. This is joint work with Imin Chen, Sander Dahmen, and Soroosh Yazdani.
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UBC
Fri 21 Oct 2011, 3:00pm
Department Colloquium
MATX 1100
hp-Adaptive finite element methods
MATX 1100
Fri 21 Oct 2011, 3:00pm-4:00pm

Abstract

We develop hp-adaptive finite element schemes for the numerical approximation of linear second-order elliptic boundary-value problems. We begin by reviewing some classical results from the late eighties. Then we show that on geometrically and anisotropically refined meshes in three dimensional polyhedral domains,  hp-methods achieve exponential rates of  convergence in the number of degrees of freedom,  thereby proving a longstanding conjecture in the theory of hp-finite element methods. In the last part of the talk, we discuss some recent results related to fully automated hp-adaptivity and illustrate numerically that our proposed adaptive refinement strategies lead to exponential rates of convergence. The talk includes work done with my former Ph.D. student Liang Zhu.
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University of Ottawa
Mon 24 Oct 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Equivariant pretheories and invariants of torsors
WMAX 110
Mon 24 Oct 2011, 3:10pm-4:10pm

Abstract

We will introduce and study the notion of an equivariant pretheory. Basic examples include equivariant Chow groups, equivariant K-theory and equivariant algebraic cobordism. As an application we generalize the theorem of Karpenko-Merkurjev on G-torsors and rational cycles; to every G-torsor E and a G-equivariant pretheory we associate a graded ring which serves as an invariant of E. In the case of Chow groups this ring encodes the information concerning the motivic J-invariant of E and in the case of Grothendieck's K_0 -- indexes of the respective Tits algebras.
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Marc Carnovale
UBC
Mon 24 Oct 2011, 4:00pm
Harmonic Analysis Seminar
MATX 1102
An exposition of the bilinear approach to the Falconer distance problem
MATX 1102
Mon 24 Oct 2011, 4:00pm-5:00pm

Abstract


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Mathematics Department, UBC
Tue 25 Oct 2011, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 110
Modelling Hydraulic Fractures using a Boundary Element Method (BEM) and the Extended Finite Element Method (XFEM)
WMAX 110
Tue 25 Oct 2011, 12:30pm-1:30pm

Abstract

This talk presents the development of BEM and XFEM frameworks for modelling hydraulic fractures, which arise in a wide range of geoengineering applications. The mathematical formulation of the problem involves a system of coupled nonlinear partial differential equations with a moving boundary, arising from the coupling between the fluid flow in the evolving fracture and the deformation of the parent material. Each of the discussed approaches has its own advantages: the BEM can efficiently simulate a propagating crack in linear homogeneous domains, while the XFEM is able to model complex settings such as multiple fractures in porous and layered rocks or plastic material deformation. The first part of the talk presents a BEM algorithm coupled with the finite-volume fluid flow model. An example of a near-surface radial crack is investigated, for which the required Green’s functions, that represent the crack as a distribution of material discontinuities, are derived. A comparison of the numerical results generated by this numerical model with data from laboratory experiments identifies particular physical phenomena that have to be accounted for in the mathematical formulation for accurately capturing the complex fracture propagation process.
In the second part of the talk, an XFEM approach to this problem is discussed. The development includes derivation of shape functions that enrich the underlying finite element formulation by representing discontinuities and singularities associated with the hydraulically driven crack. An example is presented in which a coupled XFEM model simulates a crack driven by a viscous fluid through a layered material.
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George Bluman
UBC
Tue 25 Oct 2011, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Some recent developments in symmetries and conservation laws for PDEs: Part III: conservation laws
Math Annex 1118
Tue 25 Oct 2011, 2:30pm-3:30pm

Abstract

It will be shown how to find directly all conservation laws for a given PDE system.  A consequence is the extension of the classical Noether theorem to non-variational systems.  Connections to Noether's theorem and connections between symmetries and conservation laws will be discussed.
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Universite Libre de Bruxelles
Tue 25 Oct 2011, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
PIMS (WMAX 110)
A rough guide to reduction methods for strongly coupled elliptic systems
PIMS (WMAX 110)
Tue 25 Oct 2011, 3:30pm-4:30pm

Abstract

In this talk, I will first recall the notions of superlinearity and subcriticality for strongly coupled elliptic systems. I will present various functional frameworks and their limitations. I will then discuss two reduction methods that allow to get rid of the indefiniteness of the energy functional. These reductions to a single equation are powerful to treat basic questions for superlinear systems. For instance, I will discuss the notion of ground states, in bounded domains and in R^N, show how to get the information on the symmetry and the sign of the ground states through the definition of a convenient Nehari manifold or constrained minimization problem. I will also discuss the classical question of existence of infinitely many critical points of perturbed indefinite symmetric functionals and how one of the reduction method allow to use the notion of Morse index. Finally, I will show how these reduction methods can help in proving partial symmetry and symmetry breaking. As a paradigm, I will illustrate the ideas on the Lane-Emden system with Hénon weights. 
 
References : B.-Ramos ANIHP 2009 - B.-dos Santos JDE 2010 - B.-Ramos-dos Santos Trans. AMS 2012 & preprint.    
 
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University of Ottawa
Tue 25 Oct 2011, 4:00pm
Algebraic Groups and Related Structures
Math 126
Basic polynomial invariants, fundamental representations and the Chern class map
Math 126
Tue 25 Oct 2011, 4:00pm-5:00pm

Abstract

Consider a crystallographic root system together with its Weyl group W acting on the weight lattice M. Let Z[M]^W and S^*(M)^W be the W-invariant subrings of the integral group ring Z[M] and the symmetric algebra S^*(M) respectively. A celebrated theorem of Chevalley says that Z[M]^W is a polynomial ring over Z in classes of fundamental representations w_1,...,w_n and S^*(M)^{W} over rational numbers is a polynomial ring in basic polynomial invariants q_1,...,q_n, where n is the rank. In this talk we will establish and investigate the relationship between w_i's and q_i's over the integers.
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Dartmouth
Wed 26 Oct 2011, 3:00pm
Probability Seminar
MATH 126
Edge-Cover by Random Walk
MATH 126
Wed 26 Oct 2011, 3:00pm-4:00pm

Abstract

We show that the time for a random walk to cover all
the edges of a graph with m edges is bounded by 2m^2;
if all edges must be covered in both directions, 3m^2.
These results generalize to graphs with edge-lengths
(even with infinitely many vertices) and to Brownian
motion.
Joint work with Agelos Georgakopoulos.
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The University of Texas at Austin
Wed 26 Oct 2011, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)
The density conjecture and a short survey on Kleinian groups
WMAX 216 (PIMS)
Wed 26 Oct 2011, 3:00pm-4:00pm

Abstract

I will try to give a short survey of some of the major results in the study of Kleinian groups in recent years. We will concentrate on the proof of the Bers' Density Conjecture and I will try to give an outline of the proof based on a joint work with J. Souto.
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UBC
Wed 26 Oct 2011, 4:00pm
Undergraduate Colloquium
MATH 225
Deforming complicated plane curves to simple ones
MATH 225
Wed 26 Oct 2011, 4:00pm-5:00pm

Abstract

The curve­ shortening flow has been much studied in differential geometry over the past 25 years. In this talk we will introduce the problem, 
which involves the flow of a plane curve in the normal direction with speed equal to the curvature. It was shown by M. Grayson in 1987 that 
the flow converts an arbitrary "nice" closed curve into a circle! Over the next 10 years Grayson's proof was clarified and simplified by 
R. Hamilton and G. Huisken.

We will describe the main ingredient in these simplifications, which involves finding a geometric quantity that is "improved" under the flow 
and prevents the formation of certain types of singularities. Although this is a hard theorem, its proof uses only two ­variable calculus 
together with a lot of cleverness. The curve ­shortening flow is the simplest of several geometric flows whose study is a topic of current 
research interest in differential geometry. These flows have certain features and methods in common, particularly with regard to the 
formation of singularities.

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Dartmouth
Fri 28 Oct 2011, 3:00pm
Department Colloquium
MATX 1100
Scheduling, Percolation, and the Worm Order
MATX 1100
Fri 28 Oct 2011, 3:00pm-4:00pm

Abstract

We show that in any submodular system there is a maximal chain that is minimal, in a very strong sense, among all paths from 0 to 1. The consequence is a set of general conditions under which optimal
scheduling can be done without backward steps. Among the applications are a fast algorithm for scheduling multiple processes without overusing a resource; a theorem about searching for a lost child in a forest; and a closed-form expression for the probability of escaping from the origin in a form of coordinate percolation. Joint work in part with Graham Brightwell (LSE) and in part with Lizz Moseman (NIST).
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Institut de Mathematiques de Jussieu
Mon 31 Oct 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Somekawa's K-groups and Voevodsky's Hom groups
WMAX 110
Mon 31 Oct 2011, 3:10pm-4:10pm

Abstract

We construct an isomorphism from Somekawa's K-group associated to a finite collection of semi-abelian varieties (or more general sheaves) over a perfect field to a corresponding Hom group in Voevodsky's triangulated category of effective motivic complexes.
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