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 Events
Christian Schnell
University of Illinois Chicago
Mon 1 Feb 2010, 3:00pm
Algebraic Geometry Seminar
PIMS 110
Complex analytic Neron models
PIMS 110
Mon 1 Feb 2010, 3:00pm-4:00pm

Abstract

I will present a global construction of the Neron model for degenerating families of intermediate Jacobians; a classical case would be families of abelian varieties. The construction is based on Saito's theory of mixed Hodge modules; a nice feature is that it works in any dimension, and does not require normal crossing or unipotent monodromy assumptions. As a corollary, we obtain a new proof for the theorem of Brosnan-Pearlstein that, on an algebraic variety, the zero locus of an admissible normal function is an algebraic subvariety.
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MIT
Mon 1 Feb 2010, 4:00pm SPECIAL
Department Colloquium
MATX 1100
The Picard Group of the Moduli Space of Curves with Level Structures
MATX 1100
Mon 1 Feb 2010, 4:00pm-5:00pm

Abstract

 The Picard group of an algebraic variety $X$ is the set of complex line bundles over $X$. In this talk, we will describe the Picard groups of certain finite covers of the moduli space of curves. The methods we use combine ideas from algebraic geometry, finite group theory, and algebraic/geometric topology.
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Mathematics, Virginia Tech
Tue 2 Feb 2010, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 216
Multilevel preconditioners for simulations and optimization on dynamic, adaptive meshes
WMAX 216
Tue 2 Feb 2010, 12:30pm-2:00pm

Abstract

For the efficient solution of large, sparse, linear systems of equations, Ax = b, we usually need a preconditioning matrix P, in an appropriate sense close to the inverse of A, such that solving PAx = Pb converges fast. If we need to solve a sequence of problems in which the matrix A changes slowly (and the right hand side b arbitrarily), we would like to adapt the preconditioner rather than compute a new one from scratch for each problem.

After a brief introduction to iterative linear solvers, we discuss adaptive preconditioners for time-dependent simulations and nonlinear optimization problems (topology optimization) with dynamic mesh adaptation. Adaptive meshing greatly reduces the computational cost of simulations and optimization. Unfortunately, it also carries a number of problems for preconditioning in iterative linear solvers, as changes in the mesh lead to structural changes in the linear systems we must solve. As a result, a new preconditioner must be computed after every change in the mesh, which might be prohibitively expensive. Here, we propose preconditioners that are cheap to update for dynamic changes to the mesh as well as for changes in the matrix due to nonlinearity of the underlying problem; more specifically, we propose preconditioners that require only local changes to the preconditioner for local changes in the mesh and nonlinear terms. Our preconditioners combine sparse approximate inverses with multilevel correction. For further information see [1,2].

[1] Shun Wang and Eric de Sturler, Multilevel sparse approximate inverse preconditioners for adaptive mesh refinement. Linear Algebra Appl., 431:409-426, 2009.

[2] Shun Wang, Krylov subspace methods for topology optimization on adaptive meshes. PhD thesis, University of Illinois at Urbana-Champaign, Department of Computer Science, September 2007. Advisor: Eric de Sturler, Co-Advisor: Glaucio H. Paulino.

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MIT
Tue 2 Feb 2010, 3:00pm SPECIAL
Topology and related seminars
216 WMAX
An infinite presentation for the Torelli group
216 WMAX
Tue 2 Feb 2010, 3:00pm-4:00pm

Abstract

The Torelli group is the subgroup of the mapping class group of a surface
which acts trivially on the surface's first homology group. Despite the
pioneering work of Birman, Johnson, and many others numerous basic
questions about it remain open. I will begin by describing some history
and background, and then I will discuss a new (infinite) presentation of
the Torelli group whose generators and relations have simple topological
interpretations.
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Jozsef Solymosi
UBC
Tue 2 Feb 2010, 4:00pm
Discrete Math Seminar
WMAX 216
Extremal metric problems in Discrete Geometry
WMAX 216
Tue 2 Feb 2010, 4:00pm-5:00pm

Abstract

 
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University of Toronto
Wed 3 Feb 2010, 3:00pm SPECIAL
Department Colloquium
WMAX 110
Probability in the PDE theory
WMAX 110
Wed 3 Feb 2010, 3:00pm-4:00pm

Abstract

In this talk, we discuss how probabilistic ideas are applied to study PDEs. First, we briefly go over the basic theory of Gaussian Hilbert spaces and abstract Wiener spaces to determine function spaces which capture the regularity of the Brownian motion and the white noise.  Next, we go over Bourgain's idea to establish the invariance of Gibbs
measures for PDEs. We then establish local well-posedness (LWP) of KdV with the white noise as initial data via the second iteration introduced by Bourgain. This in turn provides almost sure global well-posedness (GWP) of KdV as well as the invariance of the white noise. Then, we discuss how one can use the same idea to obtain LWP of the stochastic KdV with additive space-time (non-smoothed) white noise in the periodic setting.

 We also consider the weak convergence problem of the grand canonical ensemble (i.e. the interpolation measure of the usual Gibbs measure and the white noise) with a small parameter (tending to 0) to the white noise. This result, combined with the GWP in $H^{-1}$ by Kappeler and Topalov, provides another proof of the invariance of the white noise for KdV. In this talk, we discuss the same weak convergence problem for mKdV and cubic NLS, which provides the ``formal'' invariance of the white noise. This part is a joint work with J. Quastel and B. Valk\'o.

Lastly, if time permits, we discuss the well-posedness of the Wick ordered cubic NLS on the Gaussian ensembles below $L^2$. The main ingredient is nonlinear smoothing under randomization of initial data. For GWP, we also use the invariance (of the Gaussian ensemble) under the linear flow. This part is a joint work with J. Colliander.
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Akos Magyar
UBC
Wed 3 Feb 2010, 3:00pm
Harmonic Analysis Seminar
MATH 125
Working seminar: The U^3 inverse theorem (continued)
MATH 125
Wed 3 Feb 2010, 3:00pm-4:00pm
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Bud Homsy
UBC
Wed 3 Feb 2010, 3:00pm
Undergraduate Colloquium
MATH 105
Undergraduate Colloquium: Fluid motion and the Navier-Stokes Equations
MATH 105
Wed 3 Feb 2010, 3:00pm-4:00pm

Abstract

The next UBC/UMC talk is by Bud Homsy, Deputy Director of PIMS.

Title: Fluid motion and the Navier-Stokes Equations: Why is F=ma so tough for fluids and why haven't we solved these equations yet?

The differential equations governing the flow of fluids like air and water have been known since the 1800’s. Yet they have proven to be nearly impenetrable to mathematical analysis and to solutions using supercomputers. This talk will show many examples (in the form of movies) of physical flows from science, technology and everyday life that one would like to be able to describe. I will then give the highlights of how the Navier-Stokes equations are derived and what makes them so tough to solve.

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Jesse Goodman
UBC
Wed 3 Feb 2010, 4:00pm
Probability Seminar
WMAX 216
Exponential growth of ponds in invasion percolation on regular trees
WMAX 216
Wed 3 Feb 2010, 4:00pm-5:00pm

Abstract

In invasion percolation, the edges of a graph are assigned i.i.d. edge weights, and an infinite cluster is grown by recursively adding the boundary edge of minimal weight. By considering the edges whose weight is larger than all subsequently accepted weights, the invasion cluster is divided into a chain of ponds linked by outlets.

Working on the regular tree, we show that the sizes of the ponds grow exponentially, with law of large numbers, central limit theorem and large deviation results, and also give asymptotics for the size of a fixed pond.

We compare with known results for Z^2 and explore why these results should be expected on more general graphs.
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Anne de Roton
PIMS
Thu 4 Feb 2010, 2:00pm
PIMS Seminars and PDF Colloquiums
WMAX 216
Roth's theorem in the primes
WMAX 216
Thu 4 Feb 2010, 2:00pm-3:15pm

Abstract

In 1953, K. Roth proved that any subset of positive integers of positive density contains infinitely many non-trivial three-term arithmetic progressions. (By a non-trivial arithmetic progression we mean one of the form (a, a+d, a+2d) with d > 0.) First, I shall explain the main ideas of the proof of Roth's theorem. The second part of my talk will be devoted to Roth's theorem in the primes. I shall explain how B. Green proved that a subset of primes of positive relative density must contain some non-trivial 3-term arithmetic progressions and how H. Helfgott and I sharpened his quantitative result.

This talk is aimed to a non-specialist public.

Note for Attendees

Tea and cookies afterwards!
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John W. M. Bush
Department of Mathematics, Massachusetts Institute of Technology
Thu 4 Feb 2010, 3:15pm SPECIAL
Institute of Applied Mathematics
Angus 308
The Fluid Trampoline: Droplets Bouncing on a Soap Film (an IAM-PIMS-MITACS Distinguished Colloquium Series)
Angus 308
Thu 4 Feb 2010, 3:15pm-4:15pm

Abstract

We present the results of a combined experimental and theoretical investigation of droplets falling onto a horizontal soap film. Both static and vertically vibrated soap films are considered. A quasi-static description of the soap film shape yields a force-displacement relation that allows us to model the film as a nonlinear spring, and yields an accurate criterion for the transition between droplet bouncing and crossing. On the vibrating film, a variety of bouncing behaviours were observed, including simple and complex periodic states, multiperiodicity and chaos. A simple theoretical model is developed that captures the essential physics of the bouncing process, reproducing all observed bouncing states. The system is among the very simplest fluid mechanical chaotic oscillators. The relevance of our model to a seemingly unlikely biological system is discussed.
 
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University of Toronto
Thu 4 Feb 2010, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar / Probability Seminar
WMAX 110
Well-posedness of stochastic PDEs
WMAX 110
Thu 4 Feb 2010, 3:30pm-4:30pm

Abstract

In this talk, we first discuss the second iteration argument introduced by Bourgain to establish LWP of KdV with measures as initial data. Then, we establish LWP of the stochastic KdV (SKdV) with additive space-time white noise by estimating the stochastic convolution via Ito calculus and showing its continuity via the factorization method. Next, we discuss
well-posedness of SKdV with multiplicative noise in $L^2$. In order to treat the non-zero mean case, we derive a coupled system of a SDE and a SPDE.

Lastly, as a toy model to study KPZ equation and stochastic Burgers equation, we study stochastic KdV-Burgers equation (SKdVB). We discuss how Fourier analytic technique can be applied to show LWP. If time permits, we discuss how one can obtain global well-posedness of these equations via (1) analogue of conservation laws, (2) Applying Bourgain's argument for invariant measures (for deterministic PDEs) to SPDEs.
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Alia Hamieh and Vishaal Kapoor
UBC
Thu 4 Feb 2010, 3:30pm
One Time Event
MATH 225
Difficult Matters
MATH 225
Thu 4 Feb 2010, 3:30pm-4:30pm

Details

This is the second talk in the teaching seminar associated with the TA Accreditation Program. (All are welcome!) Graduate students will have their attendance credited toward their eventual accreditation.

Title: Difficult Matters

We will address some of the conceptual aspects of teaching mathematics by raising various pedagogical and management issues. We will explore these issues through group consideration and analysis of case studies developed by Solomon Friedberg and his team in the Mathematics Department of Boston College. These case studies have been used at universities including Boston University, Brown, Cornell, Harvard, Stanford and Dartmouth, as a tool in TA training programs for mathematics graduate teaching assistants.

We hope to have a fun and vibrant discussion, and to draw upon each others ideas, perspectives and experiences. Most importantly, this session will give us an opportunity to think in advance about these complicated situations so that we can handle them efficiently and decisively as they develop in practice.

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UBC
Mon 8 Feb 2010, 3:00pm
Algebraic Geometry Seminar
WMAX 110
What is geometrization?
WMAX 110
Mon 8 Feb 2010, 3:00pm-4:00pm

Abstract

Geometrization is a process of replacing finite sets by algebraic varieties over finite field and functions on such sets by sheaves on the corresponding variety. I will explain the meaning of the above sentence and state some applications.
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Mathematics and Mechanical Engineering, UBC
Tue 9 Feb 2010, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 216
PELICANS - an implementation tool for solver of PDEs
WMAX 216
Tue 9 Feb 2010, 12:30pm-2:00pm

Abstract

PELICANS is a C++ framework with a set of integrated reusable components, designed to simplify the task of developing applications of numerical mathematics and scientific computing. The program is developed at IRSN (France) and available under an open source license.

In this talk I will give an introduction to PELICANS starting with the Laplace equation solved by finite elements. This example is used to demonstrate how to implement your own code by choosing appropriate components of PELICANS and wiring them together. I also show that it is fairly simple to compare a given analytic solution with the numerical one for verification purposes. As another more detailed example I present the advection-diffusion equation solved by the finite volume method. Finally, some results of more complicated problems as multi-layer visco-plastic flows will be shown.

The goal of this talk is to show that PELICANS can provide you with a C++ framework which allows focusing on the set up of the mathematical description and numerical scheme rather than on the implementation. PELICANS also provides lots of examples (e.g. Navier-Stokes), it is well documented and coupled with external libraries like PETSc, SPARSKIT, and UMFPACK.

PELICANS can be downloaded from https://gforge.irsn.fr/gf/project/pelicans

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UBC
Tue 9 Feb 2010, 3:00pm SPECIAL
Topology and related seminars
216 WMAX
Orderings, eigenvalues and surgery
216 WMAX
Tue 9 Feb 2010, 3:00pm-4:00pm

Abstract

In joint work with Adam Clay, we establish a necessary condition that an automorphism of an orderable group can preserve an
ordering:  at least one of its eigenvalues, suitably defined, must be real and positive.  Applications will be given to knot theory and to the fundamental groups of fibred spaces.  An example: if surgery on a fibred knot in $S^3$ (or in a homology 3-sphere) produces a 3-manifold whose fundamental group is orderable, then the surgery must be longitudinal (0-framed) and the Alexander polynomial of the knot must have a positive real root.
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University of Chicago
Tue 9 Feb 2010, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX110
cancelled
WMAX110
Tue 9 Feb 2010, 3:30pm-4:30pm

Abstract

 
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Jochen Kuttler
University of Alberta
Tue 9 Feb 2010, 3:30pm
Algebraic Groups and Related Structures
Math 125
Singularities of Schubert varieties in the affine Grassmannian
Math 125
Tue 9 Feb 2010, 3:30pm-4:30pm

Abstract

 
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Adolfo Rodríguez
UQAM
Tue 9 Feb 2010, 4:00pm
Discrete Math Seminar
WMAX 216
Bugs, colonies, and q-Boson normal ordering
WMAX 216
Tue 9 Feb 2010, 4:00pm-5:00pm

Abstract

In my work with Miguel Mendez, we provided a new

combinatorial model for the coefficients appearing in the normal

ordering of q-Boson words, by introducing combinatorial structures

called bugs, colonies and settlements. In this lecture I will show, in

a more general context, how this kind of structures can be used to

simplify proofs of combinatorial theorems involving q-analogs, and how

our combinatorial model and formulas for the coefficients appearing in

the q-Boson normal ordering problem arise as a direct application of

these techniques.

 
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Vladimir Peller
Michigan State University
Wed 10 Feb 2010, 3:00pm
Harmonic Analysis Seminar
MATH 125
Functions of perturbed operators
MATH 125
Wed 10 Feb 2010, 3:00pm-4:00pm

Abstract

I am going to speak about my recent joint results with A.B. Aleksandrov. It
is well known that a Lipschitz function $f$ on the real line (i.e., a function $f$
satisfying the condition
$|f(x)-f(y)|\le{\rm const}\,|x-y|$) does not have to be operator Lipschitz (i.e.,
$|f(A)-f(B)|\le{\rm const}\,\|A-B\|$ for self-adjoint operators $A$ and $B$).
Surprisingly, it turns out that if $f$ is a H\"older function of order $\alpha$,
$0<\alpha<1$,
(i.e., $|f(x)-f(y)|\le{\rm const}\,|x-y|^\alpha$)
then $f$ must be operator H\"older of order $\alpha$
(i.e., $|f(A)-f(B)|\le{\rm const}\,\|A-B\|^\alpha$ for self-adjoint operators $A$ and
$B$).
We also obtain results for higher order differences and for functions of perturbed
operators in case of perturbations of Schatten-von Neumann classes.
 
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Mark Gotay
PIMS UBC
Wed 10 Feb 2010, 3:30pm
Symmetries and Differential Equations Seminar
Math Annex 1102
Stress-Energy-Momentum Tensors and the Belinfante-Rosenfeld Formula
Math Annex 1102
Wed 10 Feb 2010, 3:30pm-4:30pm

Abstract

We present a new method of constructing a stress-energy-momentum tensor for a classical field theory based on covariance considerations and Noether theory. The stress-energy-momentum tensor T^\mu_\nu that we construct is defined using the (multi)momentum map associated to the spacetime diffeomorphism group. The tensor T^\mu_\nu is uniquely determined as well as gauge-covariant, and depends only upon the divergence equivalence class of the Lagrangian. It satisfies a generalized version of the classical Belinfante-Rosenfeld formula, and hence naturally incorporates both the canonical stress-energy-momentum tensor and the ``correction terms'' that are necessary to make the latter well behaved. Furthermore, in the presence of a metric on spacetime, our T^\mu_\nu  coincides with the Hilbert tensor and hence is automatically symmetric.

This is joint work with Jerry Marsden.
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University of Regina
Wed 10 Feb 2010, 4:00pm
Probability Seminar
WMAX 216
A rate of convergence for loop-erased random walk to SLE(2)
WMAX 216
Wed 10 Feb 2010, 4:00pm-5:00pm

Abstract

Among the open problems for SLE suggested by Oded Schramm in his 2006 ICM talk is that of obtaining \reasonable estimates for the speed of convergence of the discrete processes which are known to converge to SLE." In this talk we derive a rate for the convergence of the Loewner driving function for loop-erased random walk to Brownian motion with speed 2 on the unit circle, the Loewner driving function for radial SLE(2). This talk is based on joint work with Christian Benes (CUNY) and Fredrik Johansson (KTH).

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Maxim Stykow
UBC
Thu 11 Feb 2010, 12:30pm
Graduate Student Seminar
LSK 462
What is a number?
LSK 462
Thu 11 Feb 2010, 12:30pm-1:00pm

Abstract

In this talk I will present several ideas ranging from Euclid to Conway about how to put our intuitive and also sometimes not so intuitive ideas about what a number is on a rigorous foundation. Some questions you might have that I'm going to answer are: How to create something out of nothing? Why is a proof by induction actually a proof? What is a surreal number?
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Robert Klinzmann
UBC
Thu 11 Feb 2010, 1:00pm
Graduate Student Seminar
LSK 462
What are p-adic numbers?
LSK 462
Thu 11 Feb 2010, 1:00pm-1:30pm

Abstract

 TBA
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Technische Universität Berlin
Thu 11 Feb 2010, 3:00pm
Number Theory Seminar
Room ASB10900 (IRMACS - SFU Campus)
Computing zeta functions of superelliptic curves in larger characteristic
Room ASB10900 (IRMACS - SFU Campus)
Thu 11 Feb 2010, 3:00pm-3:50pm

Abstract

Computing zeta functions of curves over finite fields is an important problem in computer algebra with connections to cryptography and coding theory, among others. In this talk, I first want to highlight how rigid cohomology can be used to construct explicit algorithms and why their runtime is usually linear in the characteristic p. In a second part, I will restrict the problem to superelliptic curves and show how the complexity can be reduced to be linear in the squareroot of p.

Note for Attendees

Refreshments will be served between the two talks.
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UBC
Thu 11 Feb 2010, 4:10pm
Number Theory Seminar
Room ASB10900 (IRMACS - SFU Campus)
Effective S-unit equations and a conjecture of Newman
Room ASB10900 (IRMACS - SFU Campus)
Thu 11 Feb 2010, 4:10pm-5:00pm

Abstract

Given a positive integer $N$, an old problem of D.J. Newman is to bound the number of ways to express $N$ as
 
N = 2^a 3^b + 2^c + 3^d
 
in nonnegative integers $a, b, c$ and $d$. That this number is finite is a consequence of a result of Evertse on $S$-units equations. That it is at most 9 requires some new ideas. I will sketch a proof of this and attempt to show how such an odd question fits into a more general framework.
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