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 Events
Ye Yang
University of Cincinnati
Tue 1 Nov 2011, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 110
An Enriched Space-Time Finite Element Method for Nonlinear Continuum Systems
WMAX 110
Tue 1 Nov 2011, 12:30pm-1:30pm

Abstract

There is a continuing interest in developing numerical methods for treating problems that are characterized by multiple time scale features. Traditional finite element method (FEM) based on semi-discrete schemes, however, is not well suited for these classes of problems due to their lack of flexibility in establishing multiscale approximations in the temporal domain. In this presentation, we show that a multiscale method that is capable of incorporating both multiple spatial and temporal features can be established based on the space-time
discontinuous Galerkin method which was originally developed in the context of linear elastodynamics. After an initial assessment of the convergence and its connection to the various time stepping algorithms, we show that space-time FEM is a stable, high-order convergent numerical method. We further explore the incorporation of fine scale features based on the extended finite element method. The nonlinear formulation incorporating enriched space-time FEM with stabilization least-square term is further developed and numerical solution based on GMRES is proposed. Through numerical examples, it is shown that multiscale space-time FEM enjoys superior convergence properties over the traditional space-time FEM and the proposed method represent a new paradigm towards resolving structural and solid mechanics problems with strong temporal nonlinearity.



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Warren Code and Joseph Lo
UBC
Tue 1 Nov 2011, 12:30pm
Mathematical Education
MATH 126
Lunch Series for Teaching and Learning: Study Skills
MATH 126
Tue 1 Nov 2011, 12:30pm-1:30pm

Abstract

This session is about student study skills:

What do we know already?  We present some recent data from a selection of first-year Math courses to look for indicators of poor study habits, and to give a sense of how widespread this issue can be.  There are indicators from other departments that some students need a boost even later on in their programs.

How do we measure them?  We will present the instruments we have used, and suggestions for collecting the same sort of data in your own class.

What are some ways to address study skill issues?  We suggest some easy-to-implement strategies to help get students on track.

We will also have time for discussion about study skills - what have you noticed among your own students, and what have you tried?

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UBC
Tue 1 Nov 2011, 2:00pm
Mathematical Education
MATX 1101
How to Conduct Class ?
MATX 1101
Tue 1 Nov 2011, 2:00pm-3:00pm

Abstract

http://wiki.ubc.ca/Sandbox:MathTeachingSeminar
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George Bluman
UBC
Tue 1 Nov 2011, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Some recent developments in symmetries and conservation laws for PDEs: Part IV. Conservation laws cont'd
Math Annex 1118
Tue 1 Nov 2011, 2:30pm-3:30pm
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UBC
Tue 1 Nov 2011, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
PIMS (WMAX 110) (Notice the date change)
Liouville-type theorems for some elliptic equations and systems
PIMS (WMAX 110) (Notice the date change)
Tue 1 Nov 2011, 3:30pm-4:30pm

Abstract

In this talk, we consider the problem of non-existence of solutions for some basic elliptic equations and systems with weights. Starting with Henon-Lane-Emden system, we present a Liouville-type theorem for bounded solutions in dimension N=3 as well as the full Henon-Lane-Emden conjecture in higher dimensions.  Since systems are normally much more complicated than equations, in higher dimensions we back to single equations (both second order and fourth order) to prove such theorems under some additional assumptions on solutions. 
 
Also, during the talk we will see many open problems. 
 
This work has been done under supervision of N. Ghoussoub.


 
 
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Institut de Mathematiques de Jussieu
Tue 1 Nov 2011, 4:00pm
Algebraic Groups and Related Structures
Math 126
On the classifying space of a linear algebraic group
Math 126
Tue 1 Nov 2011, 4:00pm-5:00pm

Abstract

On the classifying space of a linear algebraic group.
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Vasu Tewari
UBC
Tue 1 Nov 2011, 4:00pm
Discrete Math Seminar
Matx 1102
Combinatorial computation of certain Kronecker coefficients
Matx 1102
Tue 1 Nov 2011, 4:00pm-5:00pm

Abstract



It is a long standing open problem in algebraic combinatorics to compute the Kronecker coefficients of the symmetric group using a combinatorial rule. In this talk I will discuss explicit combinatorial formulae (for 5 new cases) for Kronecker coefficients arising in the inner tensor product of two Schur functions indexed by near-rectangular partitions of small height. As an application of the description of Kronecker coefficients thus obtained, I will also also describe an enumerative formula for a specific case of counting Standard Young tableaux of bounded height in terms of Catalan and Motzkin numbers.
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Sara Hormozi
Wed 2 Nov 2011, 2:00pm
Complex Fluids Seminar
MATX 1118
Visco-plastic Lubrication: From Theory to Application
MATX 1118
Wed 2 Nov 2011, 2:00pm-3:00pm

Abstract

Interfacial instabilities of multi-layer shear flows may be eliminated by
astute positioning of yield stress fluid layers that remain unyielded at
the interface(s). This lecture consists of three parts.
                                                                               
Firstly, I present a computational study of these flows in the setting of
a Newtonian core fluid surrounded by a Bingham lubricating fluid, within
pipe and channel configurations. The simulations include an inlet geometry
in the computational model and study the multi-layer flows, both as the
fluids are initially injected (start up) and later the established steady
flows (development lengths). Nonlinear perturbations are also studied,
showing in particular that during energy decay of stable perturbations the
initial rapid decay of the perturbation kinetic energy relates to
reforming/breaking of the unyielded plug and is followed by slower viscous
decay. For axisymmetric perturbations these flows can be stable to order
unity initial perturbation amplitudes and for Re<100. The channel geometry
allows for symmetry breaking and appears to be less stable. A number of
interesting effects are explored using the channel geometry.
                                                                               
Secondly, I focus on demonstrating whether the stable core annular flow can
be achieved when lubricating a visco-elastic core fluid with a yield stress
fluid. Over 100 experiments have been performed using Carbopol solutions as
the lubricating yield stress fluid and Polyethylene Oxide solutions as the
visco-elastic fluid.
                                                                               
Thirdly, I will briefly explain application of energy stability method to
study nonlinear stability of a core-annular flow of an Oldroyd-B fluid
surrounded by a Bingham fluid. Together with the experimental study, this
shows that visco-elasticity is not a barrier to use of this methodology.
                                                                               
                                                                               
Contributors: S. Hormozi(1,2), I.A. Frigaard(1,2), K. Wielage-Burchard(2) &
D.M. Martinez(3)
                                                                               

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UBC
Wed 2 Nov 2011, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)
Equivariant K-theory for Actions with Maximal Rank Isotropy
WMAX 216 (PIMS)
Wed 2 Nov 2011, 3:00pm-4:00pm

Abstract

Let G denote a compact connected Lie group with torsion-free fundamental group acting on a compact space X such that all the isotropy subgroups are connected and of maximal rank. Let T be a maximal torus with Weyl group W. We derive conditions on the induced action of W on the fixed-point set of T which imply that the equivariant K-theory of X is a free module over the representation ring of G. This can be applied to compute the equivariant K-theory of spaces of ordered commuting elements in certain compact Lie groups. This is joint work with J.M.Gomez.
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UBC
Wed 2 Nov 2011, 3:00pm
Probability Seminar
MATH 126
Rate of convergence for Cardy's formula
MATH 126
Wed 2 Nov 2011, 3:00pm-4:00pm

Abstract

We show that crossing probabilities in 2D critical
percolation converge at a polynomial rate in the mesh size to their
limit given by the Cardy-Smirnov formula. We then use this to obtain
that in the half plane the probability that the cluster at the origin
has diameter R decays like R^{-1/3} with polylogarithmic corrections,
improving the previously known estimate of R^{-1/3+o(1)}.

Joint work with Dana Mendelson, Scott Sheffield and Sam Watson.
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Wed 2 Nov 2011, 4:00pm
One Time Event
Some recnet
Wed 2 Nov 2011, 4:00pm-10:00am
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Panel Discussion
Thu 3 Nov 2011, 12:30pm
Graduate Student Seminar
LSK 460
Graduate Student Colloquium
LSK 460
Thu 3 Nov 2011, 12:30pm-2:00pm

Abstract


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UBC
Thu 3 Nov 2011, 3:00pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
Primitive sets
Room WMAX 216 (PIMS - UBC Campus)
Thu 3 Nov 2011, 3:00pm-3:50pm

Abstract

A primitive set is a set of positive integers with the property that no element of the set divides another. We review a 1934 result of Besicovitch, showing that certain primitive sets can have large upper density even though their counting function is usually small, and a 1935 result of Erdős, showing that the sum of 1/(n log n) over all elements n of a primitive set is bounded by an absolute constant. We go on to describe two new theorems on primitive sets. First, in joint work with Carl Pomerance, we construct primitive sets with consistently large counting functions (as opposed to occasionally large as in Besicovitch's example), essentially providing a converse to Erdős's theorem. Second, the optimal absolute constant in Erdős's theorem is conjectured to be the sum of 1/(p log p) over all primes p, but this conjecture is still open; we describe current joint work with Bill Banks that makes progress towards this conjecture.

Note for Attendees

Refreshments will be served between the two talks.
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Radhika Ganapathy
Purdue University
Thu 3 Nov 2011, 4:10pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
Extensions of the Deligne-Kazhdan philosophy and applications
Room WMAX 216 (PIMS - UBC Campus)
Thu 3 Nov 2011, 4:10pm-5:00pm

Abstract

Deligne and Kazhdan used the notion of close local fields to establish a way of analyzing representations of Galois groups and Algebraic groups over fields of characteristic p, using information about corresponding representations in characteristic 0.  I will first explain this theory and some related results. Then I will state our results on the extension of Kazhdan's and Howe's work on Hecke Algebra isomorphims. I will also explain how this extension has enabled us to generalize Lemaire's work on generic representations of Gln(F) over close local fields.
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Barnard College and Stony Brook
Fri 4 Nov 2011, 3:00pm
Department Colloquium
MATX 1100
PIMS/UBC Distinguished Colloquium, Embedding questions in symplectic geometry
MATX 1100
Fri 4 Nov 2011, 3:00pm-4:00pm

Abstract

As has been known since the time of Gromov's Nonsqueezing Theorem, symplectic embedding questions lie at the heart of symplectic geometry. In the past few years we have gained significant new insight into the question of when there is a symplectic embedding of one basic geometric shape (such as a ball or ellipsoid) into another (such as an ellipsoid or torus).  After a brief introduction to symplectic geometry, this talk will describe some of this progress, with particular emphasis on results in dimension four.
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Barnard College and Stony Brook
Mon 7 Nov 2011, 1:00pm SPECIAL
Topology and related seminars
WMAX 216 (PIMS)
Displaceability in symplectic toric manifolds
WMAX 216 (PIMS)
Mon 7 Nov 2011, 1:00pm-2:00pm

Abstract

Diffeomorphisms that preserve a symplectic structure have unexpected rigidity properties.  In particular, many manifold have subsets that cannot be displaced (i.e. moved to a disjoint position) by a symplectic isotopy though they can be smoothly displaced. Toric manifolds provide a good setting in which to study these questions because they have a purely combinatorial description.
 
This talk will describe some recent progress in understanding which toric fibers can be displaced.  I will try to make the subject accessible to those who do not know toric or symplectic geometry.
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George Papanicolaou
Stanford
Mon 7 Nov 2011, 3:00pm SPECIAL
Department Colloquium
MATX 1100
The Hugh C. Morris Lecture: Uncertainty quantification and systemic risk
MATX 1100
Mon 7 Nov 2011, 3:00pm-4:00pm

Abstract

The quantification of uncertainty in large-scale scientific and engineering computations is rapidly emerging as a research area that poses some very challenging fundamental problems which go well beyond sensitivity analysis and associated small fluctuation theories. We want to understand complex systems that operate in regimes where small changes in parameters can lead to very different solutions. How are these regimes characterized? Can the small probabilities of large (possibly catastrophic) changes be calculated? These questions lead us into systemic risk analysis, that is, the calculation of probabilities that a large number of components in a complex, interconnected system will fail simultaneously.

I will give a brief overview of these problems and then discuss in some detail two model problems. One is a mean field model of interacting diffusions and the other a large deviation problem for conservation laws. The first is motivated by financial systems and the second by problems in combustion, but they are considerably simplified so as to carry out a mathematical analysis. The results do, however, give us insight into how to design numerical methods where detailed analysis is impossible.


Note for Attendees

This talk will be preceded by a reception at 2:00 pm in Math 125.
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University of Alberta
Mon 7 Nov 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Rost nilpotence for surfaces
WMAX 110
Mon 7 Nov 2011, 3:10pm-4:10pm

Abstract

Let X be a smooth projective scheme over a field F. We say that Rost nilpotence is true for X in the category of Chow motives with integral coefficients if for any field extension E/F the kernel of 

CH_2(S x S)  --> CH_2(S_E x S_E)

consists of nilpotent correspondences. In my talk I will present a proof of Rost nilpotence for surfaces over fields of characteristic zero which uses Rost's theory of cycle modules.
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Robert Kircheis
IWR, University of Heidelberg, Germany
Tue 8 Nov 2011, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 110
Numerical Methods for Parameter Estimation and Optimum Experimental Design for Nonlinear PDE Models
WMAX 110
Tue 8 Nov 2011, 12:30pm-1:30pm

Abstract

To fit a model of a process described by a system of Partial Differential Algebraic Equations to a given set of experimental data we have to solve constrained, nonlinear parameter estimation problems. Since the data usually contains statistical errors the parameters are random variables too. The uncertainty of a parameter estimation can be quantified by the variance-covariance matrix of the estimator.

For minimizing the confidence region of the parameter estimation an optimized experimental setup is needed. We present our approach for the minimization of quality criteria on the variance-covariance matrix of the parameters. Thereby process controls and the layout of measurements are the optimization variables.

Our approach are derivative based optimization strategies. We introduce the general Optimum Experimental Design optimization problem and the methods implemented in the software package VPLAN, such as Quasi-Newton methods, tailored derivative evaluation by Internal Numerical Differentiation and Automatic Differentiation and exploitation of multiple experiment structures. To use experimental design for practical problems, we have developed strategies including robustification, multiple experiment formulations, a sequential strategy and an online-approach.

In the second part of the talk we give an overview of parameter estimation methods to fit the parameters to the data. We treat this kind of problems by (reduced) Gauss-Newton-Type methods and multiple-shooting. Furthermore, we will give a short outlook on what is next to come (multiple shooting for OED, Proper Orthogonal Decomposition (POD) and reduced approach).
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George Bluman
UBC
Tue 8 Nov 2011, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Some recent developments in symmetries and conservation laws for PDEs. Part V.
Math Annex 1118
Tue 8 Nov 2011, 2:30pm-3:30pm

Abstract

In Part V, we show how one can use a symmetry (discrete or continuous) of a given PDE system to map a given conservation law into another conservation law--in particular, a recently found simple and explicit formula will be presented. In addition, we show how one can use symmetries and conservation laws to determine whether a given nonlinear PDE system can be invertibly mapped to a linear PDE system and also show how to find such a mapping when it exists.
 
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University of Alberta
Tue 8 Nov 2011, 4:00pm
Algebraic Groups and Related Structures
Math 126
Rost nilpotence: Results and applications
Math 126
Tue 8 Nov 2011, 4:00pm-5:00pm

Abstract

In this talk I will discuss the notion of Rost nilpotent and point out some of its applications to quadratic forms or projective homogeneous varieties.
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Ruiyuan(Ronnie) Chen
UBC, 3rd year Hons. Math and CPSC
Tue 8 Nov 2011, 4:00pm
Discrete Math Seminar
MATX 1102
Forbidden Submatrices
MATX 1102
Tue 8 Nov 2011, 4:00pm-5:00pm

Abstract

 We consider an extremal problem arising from forbidding a submatrix. Let F be
a given (0,1)-matrix. Let avoid(m,F) denote the set of m-rowed
(0,1)-matrices with no repeated columns and no submatrix F. Here we are
concerned with row and column order. Let f(m,F) denote the maximum number
of columns among all matrices in avoid(m,F). A conjecture of Anstee,
Frankl, Furedi and Pach is that if F has k row, them there is a constant
c(F) so that f(m,F)<c(F)m^k. We make progress in the case k=2 using an
`amortized' analysis. This represents joint work with Richard Anstee and
Attila Sali.
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University of Utah
Wed 9 Nov 2011, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)
Minimal Algebraic Laminations and Arational Trees
WMAX 216 (PIMS)
Wed 9 Nov 2011, 3:00pm-4:00pm

Abstract

Associated to a tree T in the boundary of Outer space is a symbolic dynamical system called the dual lamination of T, denoted L^2(T).  We develop a two-part inductive procedure for studying L^2(T).  One part is known: it is a slight generalization of the Rips machine as developed by Coulbois-Hilion; the other part is new: it is a generalization of the classical Rauzy-Veech induction.  As an application we characterize trees T for which L^2(T) is minimal.  As a further application we give a description of the Gromov boundary of the complex of free factors: it is the space of measure classes of arational trees. (Jointly with T. Coulbois and A. Hilion.)
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UBC
Wed 9 Nov 2011, 3:00pm
Probability Seminar
MATH 126
Avoidance Coupling
MATH 126
Wed 9 Nov 2011, 3:00pm-4:00pm

Abstract

Given a Markov chain, when is it possible to construct two or more copies of the chain such that they never coincide? For random walks on the complete graph we show that it is possible to couple roughly $n^{log2/log5}$ walkers for all $n$, and $n^{1/2}$ for some $n$.

Joint with Alexander E. Holroyd, James Martin, David B. Wilson and Peter Winkler.
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University of California - Irvine
Thu 10 Nov 2011, 3:00pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
Ranks of quadratic twists of elliptic curves
Room WMAX 216 (PIMS - UBC Campus)
Thu 10 Nov 2011, 3:00pm-4:00pm

Abstract

I will discuss some recent results (joint with Zev Klagsbrun and Barry Mazur) on the distribution of 2-Selmer ranks in families of quadratic twists of elliptic curves over arbitrary number fields. We study the density of twists with a given 2-Selmer rank, and obtain some surprising results on the fraction of twists with 2-Selmer rank of given parity. Since the 2-Selmer rank is an upper bound for the Mordell-Weil rank, this work has consequences for Mordell-Weil ranks in families of quadratic twists.
 
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Daniel Moseley
University of Oregon
Mon 14 Nov 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Group actions on cohomology of varieties
WMAX 110
Mon 14 Nov 2011, 3:10pm-4:10pm

Abstract

This talk will explore a technique of using equivariant cohomology to say something about the action of a group on the cohomology of a space. In particular, we will look at examples of cohomology of flag varieties and configuration spaces. Also, we will look at a family of algebras with an algebro-geometric interpretation that admits an S_n action, and use the results we developed to make progress toward a result about these algebras.

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UBC
Mon 14 Nov 2011, 4:00pm
Harmonic Analysis Seminar
MATX 1102
On the Erdos distinct distance problem in the plane
MATX 1102
Mon 14 Nov 2011, 4:00pm-5:00pm

Abstract

 This will be the first of two expository lectures on the Guth-Katz solution of the Erdos distinct distance problem in the plane. The first talk will introduce the polynomial method and focus on the "joints problem".
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Department of Mathematics, SFU
Tue 15 Nov 2011, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 110
Generalized sampling and infinite-dimensional compressed sensing
WMAX 110
Tue 15 Nov 2011, 12:30pm-1:30pm

Abstract

Compressed sensing has been one of the great successes of applied mathematics in the last decade. It allows one to reconstruct sparse signals from seemingly incomplete collections of measurements, and thereby circumvent the classical Nyquist barrier. However, compressed sensing is currently a finite-dimensional theory: it concerns the recovery of vectors in finite-dimensional vector spaces. With this in mind, the purpose of this talk is to introduce a new framework that extends the current theory and techniques to infinite-dimensional problems.

This new framework originates from recent developments in classical (i.e. Nyquist rate) signal recovery, known as generalized sampling. Generalized sampling, which I will introduce in the first part of the talk, allows for signal reconstruction in arbitrary bases in a manner which is both numerically stable and, in a certain sense, optimal. The infinite-dimensional compressed sensing framework builds on this approach by allowing one to take advantage of sparsity to obtain significant subsampling.

This is joint work with Anders Hansen (Cambridge)

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Steve Bennoun
UBC
Tue 15 Nov 2011, 2:00pm
Mathematical Education
MATX 1101
How to Conduct Class ? From Theory to Classroom Practices
MATX 1101
Tue 15 Nov 2011, 2:00pm-3:00pm

Abstract

More info under : http://wiki.ubc.ca/Sandbox:MathTeachingSeminar
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George Bluman
UBC
Tue 15 Nov 2011, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Recent developments in symmetries and conservation laws for PDEs. Part VI. Mappings
Math Annex 1118
Tue 15 Nov 2011, 2:30pm-3:30pm

Abstract

In Part VI, we will show how to solve two important mapping problems.

1, Given a nonlinear PDE system, does their exist an invertible mapping to a linear PDE system?  Find such a mapping when it exists.

2. Given a linear PDE with variable coefficients, does their exist an invertible mapping to a linear PDE system with constant coefficients?  Find the most general such mapping when it exists.
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UBC
Tue 15 Nov 2011, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (Schedule and time tentative)
Free boundary problem for embedded minimal surfaces
WMAX 110 (Schedule and time tentative)
Tue 15 Nov 2011, 3:30pm-4:30pm

Abstract

For any smooth compact Riemannian 3-manifold with boundary, we prove that there always exists a smooth, embedded minimal surface with (possibly empty) free boundary. We also obtain a priori upper bound on the genus of such minimal surfaces in terms of the topology of the ambient compact 3-manifold. An interesting note is that no convexity assumption on the boundary is required. In this talk,  we will describe the min-max construction for the free boundary problem, and then we will sketch a proof of the existence part of the theory.
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Felipe Garcia-Ramos
UBC
Tue 15 Nov 2011, 4:00pm
Discrete Math Seminar
MATX 1102
Surjective number conserving cellular automata
MATX 1102
Tue 15 Nov 2011, 4:00pm-5:00pm

Abstract

Number conserving cellular automata (NCCA) are discrete
models of particles in a grid of cells that move according to a local
rule. I will present some results for surjective one-dimensional NCCA.
For example, we will find what to expect of a reversible traffic model
with no mean drivers.
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Ian Hewitt
UBC
Wed 16 Nov 2011, 2:00pm
Complex Fluids Seminar
MATX 1118
Instabilities of a plough towed over a fluid layer
MATX 1118
Wed 16 Nov 2011, 2:00pm-3:00pm

Abstract

I will describe recent experiments in which an angled plate is dragged horizontally over a fluid surface; the plate is attached by a pivot in such a way as to be able to move freely up and down in response to the lift force from the fluid.  We find that the steady planing state, in which the plate's vertical position remains constant, becomes unstable if it is towed above a threshold speed.  Instead, the plate oscillates up and down, leaving a rippled imprint on the fluid layer.  The same instability occurs on a granular layer, and is responsible for the troublesome phenomenon of 'washboard' or 'corrugated' roads.  
 
After describing the experiments I will discuss attempts to rationalize these observations using simple theoretical models for the dynamics of the plate and the lift force provided by the deforming fluid.  Special attention will be given to yield stress fluids, for which the imprinted pattern remains 'frozen' into the surface.
 
 
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UBC
Wed 16 Nov 2011, 3:00pm
Probability Seminar
MATH 126
Gaussian upper bounds for heat kernels of continuous time simple random walks
MATH 126
Wed 16 Nov 2011, 3:00pm-4:00pm

Abstract

We consider continuous time simple random walks with arbitrary speed measure \theta on infinite weighted graphs.  Write p_t(x,y) for the heat kernel of this process.  Given on-diagonal upper bounds for the heat kernel at two points x_1,x_2, we obtain a Gaussian upper bound for p_t(x_1,x_2).  The distance function which appears in this estimate is not in general the graph metric, but a new metric which is adapted to the random walk.  Long-range non-Gaussian bounds in this new metric are also established.  Applications to heat kernel bounds for various models of random walks in random environments are discussed.

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UBC
Thu 17 Nov 2011, 11:00am
Stochastic Dynamics Working Group
IAM Lounge (LSK 306)
Evolutionary dynamics in finite populations: Stochastic differential equations versus individual based simulations
IAM Lounge (LSK 306)
Thu 17 Nov 2011, 11:00am-12:00pm

Abstract


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Iain Moyles and TBA
UBC
Thu 17 Nov 2011, 12:30pm
Graduate Student Seminar
LSK 460
Graduate Student Colloquium
LSK 460
Thu 17 Nov 2011, 12:30pm-2:00pm

Abstract


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Ecole Polytechnique Fédérale de Lausanne
Thu 17 Nov 2011, 3:00pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
Galois averages of Rankin-Selberg L-functions
Room ASB 10900 (IRMACS - SFU Campus)
Thu 17 Nov 2011, 3:00pm-3:50pm

Abstract

I will first review the notion of Galois averages of Rankin-Selberg L-functions, in particular those of Rankin-Selberg L-functions of weight-two cusp forms times theta series associated to Hecke characters of imaginary quadratic fields. I will then present a conjecture about the behaviour of these averages with the conductor of the character, of which the nonvanishing theorems of Rohrlich, Vatsal and Cornut-Vatsal are special cases. Finally, I will explain a strategy of proof, at least in the setting where the class number is equal to one.

Note for Attendees

Refreshments will be served between the two talks.
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Jason Siefken
University of Victoria
Thu 17 Nov 2011, 3:30pm
Symbolic Dynamics and Ergodic Theory Seminar
MATX 1102
Ergodic optimization of super-continuous functions on shift spaces
MATX 1102
Thu 17 Nov 2011, 3:30pm-4:30pm

Abstract

Ergodic optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that ‘most’ functions are optimized by measures supported on a periodic orbit, and it has been proved in several separable spaces that an open and dense subset of functions is optimized by measures supported on a periodic orbit. All known positive results have been for separable spaces. We give in this paper the first positive result for a non-separable space, the space of super-continuous functions on the full shift, where the set of functions optimized by periodic orbit measures contains an open dense subset.
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Carleton University
Thu 17 Nov 2011, 4:10pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
Character identities in real twisted endoscopy
Room ASB 10900 (IRMACS - SFU Campus)
Thu 17 Nov 2011, 4:10pm-5:00pm

Abstract

Part of the Langlands Program is to find a meaningful correspondence between representations of Galois groups and representations of reductive algebraic groups.  I will attempt to motivate this through an example and then concentrate on what happens at a (real) Archimedean place of the global picture.  In this context the idea of endoscopy arises in a natural fashion and suggests identities between representations of different Lie groups. These identities have been proven by Shelstad.  I will sketch the theory of endoscopy under twisting by a group automorphism and describe character identities between discrete series representations.
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University of Toronto
Mon 21 Nov 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Coverings over tori and application to Klein's resolvent problem
WMAX 110
Mon 21 Nov 2011, 3:10pm-4:10pm

Abstract

Topological essential dimension of a covering is the minimal dimension of a base-space such that the original covering can be induced from some covering over this base-space.
 
We will see how to compute the topological essential dimension for coverings over tori.
 
Surprisingly this question turns out to be useful in obtaining estimates in Klein's resolvent problem: what is the minimal number k such that the equation z^n+a_1z^n+...+a_n=0 with complex coefficients a_1,...,a_n can be reduced by means of a rational substitution y=R(z,a_1,...,a_n) to an equation on y depending on k algebraically independent parameters.
 
We will also obtain some bounds in the analogue of this question for other algebraic functions and get a sharp result for functions on C^n unramified outside of coordinate hyperplanes.
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UBC
Mon 21 Nov 2011, 4:10pm
Harmonic Analysis Seminar
MATX 1102
On the Erdos distinct distance problem in the plane
MATX 1102
Mon 21 Nov 2011, 4:10pm-5:00pm

Abstract

 The second part of the exposition of the recent solution of Erdos's distinct distance problem in the plane by Guth and Katz.
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Department of Computer Science
Tue 22 Nov 2011, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 110
Solving Laplacian Systems: Some Contributions from Theoretical Computer Science
WMAX 110
Tue 22 Nov 2011, 12:30pm-1:30pm

Abstract

This talk discusses algorithms to solve systems of linear equations where the matrix is the Laplacian matrix of a graph. These systems arise in many applications: in scientific computing, when using the finite difference method to approximately solve Poisson's equation; in machine learning, in some methods for semi-supervised learning on graphs; and in theoretical computer science, in fast algorithms for network flow problems.

For two decades, theoretical computer scientists have been developing algorithms with provable running-time bounds for solving such systems of equations. The current state-of-the-art algorithm computes a solution with relative error epsilon in the energy norm in running time O(m log n (log log n)^2 log(1/epsilon)) for any Laplacian matrix of size n x n with m non-zero entries.

These algorithms use several sophisticated tools, including low-stretch trees and concentration of random matrices. In this talk we give a survey of these results.
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Greg Mayer
UBC
Tue 22 Nov 2011, 12:30pm
Mathematical Education
MATH 126
Lunch Series for Teaching and Learning: Online Learning Tools in Undergraduate Mathematics
MATH 126
Tue 22 Nov 2011, 12:30pm-1:30pm

Abstract

This informal presentation provides an overview of current technologies that are being used at UBC to enhance student learning through online technologies, including screen casting, WeBWorK, Wolfram Alpha, UBC Blogs, and the UBC Wiki.
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Tue 22 Nov 2011, 2:30pm
One Time Event
Math
Math
Tue 22 Nov 2011, 2:30pm-3:30pm
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Tue 22 Nov 2011, 2:30pm
One Time Event
Math
Math
Tue 22 Nov 2011, 2:30pm-3:30pm
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George Bluman
UBC
Tue 22 Nov 2011, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Some recent developments in symmetries and conservation laws for PDEs. Part VII
Math Annex 1118
Tue 22 Nov 2011, 2:30pm-3:30pm

Abstract

In Part VII, we will consider two items.

1. Given a linear PDE with variable coefficients, find all forms of the variable coefficients so that the PDE can be mapped invertibly to a linear PDE with constant coefficients.  This problem was originally posed by Kolmogorov in a limited way in his celebrated paper introducing "Kolmogorov's equation".  In particular, he posed the problem of when can a diffusion process be mapped into a Wiener process.  The complete solution to this problem was found in the early 1980's using group methods.

2. The so-called nonclassical method to find systematically solutions of nonlinear PDEs.  This significantly extends Lie's work on finding invariant solutions for PDEs based on invariance under point (Lie) symmetries.  In Lie's approach, one looks for symmetries (that are invertible transformations) that map any solution of a PDE to another solution of the PDE, i.e, leave invariant the solution manifold and then seeks corresponding invariant solutions.  In the "nonclassical" approach, one seeks symmetries that leave invariant a submanifold of solutions of a given PDE (but maps other solutions of the PDE to solutions of another PDE) and then seeks corresponding invariant solutions.  This approach has proven very fruitful to discover solutions of many well-known nonlinear PDEs. 
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University of Toronto
Tue 22 Nov 2011, 4:00pm
Algebraic Groups and Related Structures
Math 126
From rational functions invertible in radicals to complex reflection groups
Math 126
Tue 22 Nov 2011, 4:00pm-5:00pm

Abstract

In 1922 J.F. Ritt classified rational functions of prime degree invertible in radicals. Since then exactly the same family of rational functions or families of rational functions closely related to it have appeared in many different parts of mathematics, for instance as commuting rational functions (with interpretation as integrable discrete dynamical systems) or as rational functions that appear in rational function analogue of Schur's conjecture in number theory.
 
We will see several characterizations of these rational functions and discuss a possible generalization of them to many dimensions. This proposed generalization is related to actions of groups generated by generalized complex reflections. For instance the polynomials among these rational functions have been previously studied under the name of "folding polynomials" because of the way they act on a fundamental domain of a real group generated by reflections.
 
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Alberto Verjovsky
UNAM Cuernavaca
Wed 23 Nov 2011, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)
Hedlund's theorem for compact, minimal laminations by surfaces with negative curvature
WMAX 216 (PIMS)
Wed 23 Nov 2011, 3:00pm-4:00pm

Abstract

I will present the ideas of a version of  a theorem of Hedlund for compact laminations (or foliations). More precisely: If L is a compact minimal Riemannian lamination by surfaces of negative curvature, we give a sufficient condition for the horocycle flow on its unit tangent bundle to be minimal, in other words every orbit of the flow is dense.
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TU Eindhoven
Wed 23 Nov 2011, 3:00pm
Probability Seminar
MATH 126
The survival probability and r-point functions in high dimensions
MATH 126
Wed 23 Nov 2011, 3:00pm-4:00pm

Abstract

We investigate the survival probability, \theta_n, in high-dimensional statistical physical models, where \theta_n denotes the probability that the model survives up to time n. Models to which our results apply are oriented percolation above 4+1 dimensions, the contact process above 4+1 dimensions, and lattice trees above 10 dimensions. We show that, similarly to branching processes, for these models, Kolmogorov's result that n\theta_n converges holds, as well as Yaglom's theorem stating that, conditionally on survival to time n, the number of particles is approximately n times an exponential random variable.

In more detail, we prove that if the r-point functions scale to those of the canonical measure of super-Brownian motion, and if a certain self-repellence conditions is satisfied, then n\theta_n->2/(AV), where a) A is the asymptotic expected number of particles alive at time n, and b) V is the vertex factor of the model. Our proofs are based on simple weak convergence arguments.

In the case of oriented percolation, this reproves a result with den Hollander and Slade (that was proved using heavy lace expansion arguments), at the cost of losing explicit error estimates.

[This is joint work with Mark Holmes, building on work with Gordon Slade, Frank den Hollander and Akira Sakai.]
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UCLA
Thu 24 Nov 2011, 3:30pm
Algebraic Groups and Related Structures
Math 104
Toric Varieties and Essential Dimension
Math 104
Thu 24 Nov 2011, 3:30pm-4:30pm

Abstract

I will discuss toric varieties over non-algebraically closed fields with applications to essential dimension.
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Jun Kitagawa
PIMS-UBC
Mon 28 Nov 2011, 3:00pm
PIMS Seminars and PDF Colloquiums
WMAX 216
The Far-Field Reflector Antenna problem, and a connection to the optimal transportation problem
WMAX 216
Mon 28 Nov 2011, 3:00pm-4:00pm

Abstract

The reflector antenna problem is the problem of constructing a reflective surface which directs a specified energy distribution (i.e. light, or radio signals) emanating from the center of a sphere to another specified energy distribution on the so-called far-field sphere. I will discuss some of the basic analytic and geometric background of this problem, and a connection that has been discovered in recent years to Monge's optimal mass transportation problem.

Note for Attendees

Tea & cookies PRECEDING the talk at 2:45 in the WMAX upstairs lounge!
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Northwestern University
Mon 28 Nov 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110
The quantum BCOV theory and higher-genus mirror symmetry
WMAX 110
Mon 28 Nov 2011, 3:10pm-4:10pm

Abstract

The physicists Bershadsky, Cecotti, Ooguri and Vafa argued that the mirror to the theory of Gromov-Witten invariants is provided by a certain quantum field theory on Calabi-Yau varieties.  I'll describe joint work in progress with Si Li, which gives a rigorous construction of the BCOV quantum field theory.  In the case of the elliptic curve, Li has shown that our theory recovers the Gromov-Witten invariants of the mirror curve, and so proving mirror symmetry in this example.

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David Kohler
UBC
Tue 29 Nov 2011, 2:00pm
Mathematical Education
MATX 1101
How Do They Treat Their Students ?
MATX 1101
Tue 29 Nov 2011, 2:00pm-3:00pm

Abstract

We'll present the sixth chapter of Bain's book on the relationship between teachers and students. All info under : http://wiki.ubc.ca/Sandbox:MathTeachingSeminar
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George Bluman
UBC
Tue 29 Nov 2011, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Some recent developments in symmetries and conservation laws for PDEs: Part VIII
Math Annex 1118
Tue 29 Nov 2011, 2:30pm-3:30pm

Abstract

The nonclassical method to find systematically solutions of nonlinear PDEs will be presented.
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Lior Silberman
UBC
Tue 29 Nov 2011, 4:00pm
Discrete Math Seminar
Matx 1102
Fixed points for Lipschitz actions of random groups
Matx 1102
Tue 29 Nov 2011, 4:00pm-5:00pm

Abstract

I will first discuss actions of finite groups on metric spaces by Lipschitz maps (maps which preserve distance up to a constant), starting with an open problem about the group with two elements.

I will then discuss the passage to infinite groups, leading to recent results on the fixed-point property for random groups in Gromov's density model.
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Harish N Dixit
UBC - Math
Wed 30 Nov 2011, 2:00pm
Complex Fluids Seminar
MATX 1118
Linear stability of vortices: transient growth and continuous spectrum
MATX 1118
Wed 30 Nov 2011, 2:00pm-3:00pm

Abstract

A vortex column supports oscillations known as Kelvin modes. These
modes only exist for vortices with a compact core. For smooth vortices, the
Kelvin modes are replaced by exponentially damped quasi-modes, a collective
response of the continuous spectrum eigenfunctions. In the first part of
this talk, we discuss the inviscid response of a 2D vortex to external
disturbances. We show that for certain initial conditions, vorticity
gradient can arrest the Landau damping process by a screening mechanism. In
the second part of the talk, we discuss a novel way to understand the
continuous spectrum of smooth 3D vortices. This is facilitated by a well
known analogy between 3D disturbances to a vortex column and disturbances in
a stratified shear flow.

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U Paris-Sud
Wed 30 Nov 2011, 3:00pm
Probability Seminar
MATH 126
Random maps and their scaling limits
MATH 126
Wed 30 Nov 2011, 3:00pm-4:00pm

Abstract

We show the convergence of large random quadrangulations, i.e. random decompositions of the sphere into a large number of quadrangles, towards the so-called Brownian map, which is a universal model for a continuum random surface. Proving this convergence, which holds in the Gromov-Hausdorff topology after proper rescaling of distances in the random map, requires a precise study of geodesics in large quadrangulations and in the limiting space, and in particular, of the locus where geodesics tend to separate.

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UCLA
Wed 30 Nov 2011, 3:00pm
Department Colloquium
MATX 1100
Mathematics of Crime
MATX 1100
Wed 30 Nov 2011, 3:00pm-4:00pm

Abstract

There is an extensive applied mathematics literature developed for problems in the biological and physical sciences. Our understanding of social science problems from a mathematical standpoint is less developed, but also presents some very interesting problems, especially for young researchers. This lecture uses crime as a case study for using applied mathematical techniques in a social science application and covers a variety of mathematical methods that are applicable to such problems. We will review recent work on agent based models, methods in linear and nonlinear partial differential equations, variational methods for inverse problems and statistical point process models. From an application standpoint we will look at problems in residential burglaries and gang crimes. Examples will consider both ``bottom up'' and ``top down'' approaches to understanding the mathematics of crime, and how the two approaches could converge to a unifying theory.

Note for Attendees

PIMS Tea will be served at 2:30 in PIMS.
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Princeton University
Wed 30 Nov 2011, 4:15pm SPECIAL
Topology and related seminars
WMAX 216 (PIMS)
Finite-sheeted covers of 3-manifolds and the Cohomology of Solenoids
WMAX 216 (PIMS)
Wed 30 Nov 2011, 4:15pm-5:15pm

Abstract

The study of finite-sheeted covering spaces of 3-manifolds has been invigorated in recent years by the resolution of several long-standing conjectures by Kahn-Markovic, Agol and Wise.  In this talk, I will discuss how using this work one can reformulate some of the central open questions in the field in terms of objects called solenoids. These objects are formed by taking inverse limits of families of finite-sheeted covering spaces of a compact manifold M, and they can be thought of as pro-finite analogues of covering spaces of M. While such an object can in general be quite complicated, I will show in this talk that if M is a compact aspherical 3-manifold, then the solenoid given by taking the inverse limit of the family of all finite-sheeted connected covering spaces of M looks like a disk from the perspective of Cech cohomology with coefficients in any finite module. I will then talk about the relevance of this result to elementary questions about finite-sheeted covers.
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