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, 3:00pm4:00pm
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 BrosnanPearlstein 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, 4:00pm5:00pm
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, 12:30pm2:00pm
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 timedependent 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., 431:409426, 2009.
[2] Shun Wang, Krylov subspace methods for topology optimization on adaptive meshes. PhD thesis, University of Illinois at UrbanaChampaign, Department of Computer Science, September 2007. Advisor: Eric de Sturler, CoAdvisor: 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, 3:00pm4:00pm
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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UBC

Tue 2 Feb 2010, 4:00pm
Discrete Math Seminar
WMAX 216

Extremal metric problems in Discrete Geometry

WMAX 216
Tue 2 Feb 2010, 4:00pm5:00pm
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, 3:00pm4:00pm
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 wellposedness (LWP) of KdV with the white noise as initial data via the second iteration introduced by Bourgain. This in turn provides almost sure global wellposedness (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 spacetime (nonsmoothed) 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 wellposedness 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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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, 3:00pm4:00pm
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UBC

Wed 3 Feb 2010, 3:00pm
Undergraduate Colloquium
MATH 105

Undergraduate Colloquium: Fluid motion and the NavierStokes Equations

MATH 105
Wed 3 Feb 2010, 3:00pm4:00pm
Abstract
The next UBC/UMC talk is by Bud Homsy, Deputy Director of PIMS.
Title: Fluid motion and the NavierStokes 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 NavierStokes equations are derived and what makes them so tough to solve.
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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, 4:00pm5:00pm
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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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, 2:00pm3:15pm
Abstract
In 1953, K. Roth proved that any subset of positive integers of positive density contains infinitely many nontrivial threeterm arithmetic progressions. (By a nontrivial 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 nontrivial 3term arithmetic progressions and how H. Helfgott and I sharpened his quantitative result.
This talk is aimed to a nonspecialist public.
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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 IAMPIMSMITACS Distinguished Colloquium Series)

Angus 308
Thu 4 Feb 2010, 3:15pm4:15pm
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 quasistatic description of the soap film shape yields a forcedisplacement 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

Wellposedness of stochastic PDEs

WMAX 110
Thu 4 Feb 2010, 3:30pm4:30pm
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 spacetime white noise by estimating the stochastic convolution via Ito calculus and showing its continuity via the factorization method. Next, we discuss
wellposedness of SKdV with multiplicative noise in $L^2$. In order to treat the nonzero 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 KdVBurgers equation (SKdVB). We discuss how Fourier analytic technique can be applied to show LWP. If time permits, we discuss how one can obtain global wellposedness 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
MATH 225

Difficult Matters

MATH 225
Thu 4 Feb 2010, 3:30pm4:30pm
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, 3:00pm4:00pm
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, 12:30pm2:00pm
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 advectiondiffusion equation solved by the finite volume method. Finally, some results of more complicated problems as multilayer viscoplastic 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. NavierStokes), 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, 3:00pm4:00pm
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 3sphere) produces a 3manifold whose fundamental group is orderable, then the surgery must be longitudinal (0framed) 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, 3:30pm4:30pm
Abstract
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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, 3:30pm4:30pm
Abstract
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UQAM

Tue 9 Feb 2010, 4:00pm
Discrete Math Seminar
WMAX 216

Bugs, colonies, and qBoson normal ordering

WMAX 216
Tue 9 Feb 2010, 4:00pm5:00pm
Abstract
In my work with Miguel Mendez, we provided a new
combinatorial model for the coefficients appearing in the normal
ordering of qBoson 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 qanalogs, and how
our combinatorial model and formulas for the coefficients appearing in
the qBoson normal ordering problem arise as a direct application of
these techniques.
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Michigan State University

Wed 10 Feb 2010, 3:00pm
Harmonic Analysis Seminar
MATH 125

Functions of perturbed operators

MATH 125
Wed 10 Feb 2010, 3:00pm4:00pm
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
$f(x)f(y)\le{\rm const}\,xy$) does not have to be operator Lipschitz (i.e.,
$f(A)f(B)\le{\rm const}\,\AB\$ for selfadjoint operators $A$ and $B$).
Surprisingly, it turns out that if $f$ is a H\"older function of order $\alpha$,
$0<\alpha<1$,
(i.e., $f(x)f(y)\le{\rm const}\,xy^\alpha$)
then $f$ must be operator H\"older of order $\alpha$
(i.e., $f(A)f(B)\le{\rm const}\,\AB\^\alpha$ for selfadjoint operators $A$ and
$B$).
We also obtain results for higher order differences and for functions of perturbed
operators in case of perturbations of Schattenvon Neumann classes.
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PIMS UBC

Wed 10 Feb 2010, 3:30pm
Symmetries and Differential Equations Seminar
Math Annex 1102

StressEnergyMomentum Tensors and the BelinfanteRosenfeld Formula

Math Annex 1102
Wed 10 Feb 2010, 3:30pm4:30pm
Abstract
We present a new method of constructing a stressenergymomentum tensor for a classical field theory based on covariance considerations and Noether theory. The stressenergymomentum 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 gaugecovariant, and depends only upon the divergence equivalence class of the Lagrangian. It satisfies a generalized version of the classical BelinfanteRosenfeld formula, and hence naturally incorporates both the canonical stressenergymomentum 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 looperased random walk to SLE(2)

WMAX 216
Wed 10 Feb 2010, 4:00pm5:00pm
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 looperased 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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UBC

Thu 11 Feb 2010, 12:30pm
Graduate Student Seminar
LSK 462

What is a number?

LSK 462
Thu 11 Feb 2010, 12:30pm1:00pm
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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UBC

Thu 11 Feb 2010, 1:00pm
Graduate Student Seminar
LSK 462

What are padic numbers?

LSK 462
Thu 11 Feb 2010, 1:00pm1:30pm
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, 3:00pm3:50pm
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.
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UBC

Thu 11 Feb 2010, 4:10pm
Number Theory Seminar
Room ASB10900 (IRMACS  SFU Campus)

Effective Sunit equations and a conjecture of Newman

Room ASB10900 (IRMACS  SFU Campus)
Thu 11 Feb 2010, 4:10pm5:00pm
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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Note for Attendees
Tea and cookies afterwards!