2011 - 2012
Calendrier des conférences / Conference Calendar
Date Heure/Time : 02/17/2012 - 16:00
Lieu/Venue : Université de Montréal, Pav. André-Aisenstadt, 2920, chemin de la Tour, SALLE 6214
Conférencier/Speaker : Olga Kharlampovich , McGill University and Hunter College CUNY
Titre/Title : Definable subsets in free and torsion free hyperbolic groups
Resume/Abstract :
We will give a survey of the results and open problems in model theory and algebraic geometry for free and hyperbolic groups. In particular, we give a description of definable (in first order logic) subsets in a free non-abelian group F that follows from our work on the Tarski problems. As a corollary we show that proper non-cyclic subgroups of F are not definable (solution of old Malcev's problem) and prove Bestvina and Feighn's result that definable subsets in a free group are either negligible or co-negligible. We prove similar results for non-elementary torsion free hyperbolic groups. This is a joint work with A. Miasnikov.
Date Heure/Time : 02/10/2012 - 16:00
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., SALLE SH-3420
Conférencier/Speaker : Ludmil Katzarkov , University of Miami and University of Vienna
Titre/Title : On the Shafarevich Conjecture
Resume/Abstract :
The Shafarevich Conjecture is the statement that the universal covering of smooth projective variety is holomophically convex, to be defined in the talk. We will discuss our result verifying the conjecture for projective varieties with linear fundamental group and suggest ways of generalizing this result.
Date Heure/Time : 02/03/2012 - 16:00
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., SALLE SH-3420
Conférencier/Speaker : Vadim Kaimanovich, University of Ottawa
Titre/Title : Equivalence relations, random graphs and stochastic homogenization
Resume/Abstract :
The theory of measured discrete equivalence relations provides a natural setup for studying infinite random graphs. We shall discuss several results related to construction and various approximations of invariant measures of the associated equivalence relations.
Date Heure/Time : 01/27/2012 - 16:00
Lieu/Venue : Université de Montréal, Pav. André-Aisenstadt, 2920, chemin de la Tour, SALLE 6214
Conférencier/Speaker : Alex Eskin, University of Chicago
Titre/Title : Rational billiards and the SL(2,R) action on moduli space
Resume/Abstract :
I will discuss ergodic theory over the moduli space of compact Riemann surfaces and its applications to the study of polygonal billiard tables. There is an analogy between this subject and the theory of flows on homogeneous spaces; I will talk about some successes and limitations of this viewpoint. This is joint work with Maryam Mirzakhani and Amir Mohammadi.
Date Heure/Time : 01/20/2012 - 16:00
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., SALLE SH-3420
Conférencier/Speaker : Jason Starr, Stony Brook
Titre/Title : Rational curves and rational points
Resume/Abstract :
There is a fruitful analogy between topology and algebraic geometry in which continuous maps from the unit interval are replaced by regular / holomorphic maps from the projective line, i.e., "rational curves". This leads to analogues in algebraic geometry of the topological notions of "path connected" and "simply connected". The holy grail is an analogue of in algebraic geometry of topological obstruction theory, giving necessary and sufficient conditions for a fibration over a base space to admit a section, i.e., a "rational point". I will explain such results when the base is a complex projective curve (joint with Graber and Harris), when the base is a complex projective surface (joint with de Jong and Xuhua He), and some recent arithmetic results when the base is a "global function field" (joint work with Chenyang Xu).
Date Heure/Time : 01/13/2012 - 16:00
Lieu/Venue : Université de Montréal, Pav. André-Aisenstadt, 2920, chemin de la Tour, SALLE 6214
Conférencier/Speaker : Louis-Pierre Arguin, Université de Montréal
Titre/Title : Probabilité et Physique Statistique des Systèmes Désordonnés
Resume/Abstract :
Dans les trente dernières années, des liens étroits se sont développés entre la physique statistique et les probabilités. Cette connexion fructueuse a mené à la découverte de structures mathématiques fondamentales. Un exemple de développement récent est la description des valeurs extrêmes de processus stochastiques en grande dimension qui s'inspire en grande partie de l'étude des modèles de physique statistique avec désordre. Dans cet exposé, je décrirai cette connexion à partir de l'exemple simple des variables indépendantes jusqu'aux développements récents pour des processus stochastiques complexes connus sous le nom de verres de spins.
Date Heure/Time : 12/16/2011 - 16:00
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., SALLE SH-3420
Conférencier/Speaker : Alan Huckleberry, Ruhr University of Bochum
Titre/Title : Disordered Bosons: A Complex Geometric Viewpoint
Resume/Abstract :
The mathematics in the talk involves the study of a concrete complex analytic setting from symplectic geometric and probabalistic viewpoints. The motivation comes from a question related to the quantum mechanics of disordered bosons. Unlike the fermionic side where the underlying Lie groups of the classical ensembles are compact, the symmetry groups for ensembles of disordered bosons are typically noncompact. In the bosonic case the basic random matrix models consist of matrices in the Lie algebra g=sp_n(R). Assuming dynamical stability, their eigenvalues are required to be purely imaginary. In the lecture we will sketch our recent work with K. Schaffert (J. Phys. A. (2011) 335207) where a method is proposed for constructing ensembles (E,P) of G-invariant sets E of such matrices with probability measures P. These arise as moment map direct images from phase spaces X which play an important role in complex geometry and representation theory. We will discuss in detail the toy-model case of n=1, where X is the complex bidisk and P is the direct image of the uniform measure.
Date Heure/Time : 12/09/2011 - 16:00
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Gilbert Strang, MIT
Titre/Title : Balanced Splitting Methods / Infinite Matrices
Resume/Abstract :
Most of this talk is about a problem that constantly arises in scientific computing. The last part is about an algebra problem -- for finite and infinite matrices. Differential equations often have diffusion and advection and reaction terms. Those are treated differently, and separately when possible. Diffusion might be implicit and advection explicit. Reaction is highly nonlinear, but local. If we separate the transport terms T(u) from the reaction terms R(u), we may "split" each time step into separate integrations. Since they don't commute, the overall step has only first-order accuracy. But second order is achieved by a half-step based on T, a full step based on R, and a half-step based on T. Problem: An error can appear in the steady state. The solution to T(u)+ R(u) = 0 may not solve T(u) = 0 and R(u) = 0 separately. Solution: Adjust to T(u) + c_n and R(u) - c_n by a balancing vector c_n at each step. If we choose c_n = (R(u_n) - T(u_n))/2 then each part can converge to the correct steady state. But stability becomes harder to ensure -- and Ray Speth has created a "rebalanced splitting" that is equally accurate and much more stable. For two problems on banded doubly infinite matrices there is progress to report: 1. Is the triangular factorization A = LPU still possible ? Notice the position of P !! 2. Which is the 'main diagonal' of that infinite matrix ?
Date Heure/Time : 12/02/2011 - 16:00
Lieu/Venue : Université de Montréal, Pav. André-Aisenstadt, 2920, chemin de la Tour, SALLE 6214
Conférencier/Speaker : Gerda de Vries, University of Alberta
Titre/Title : Formation of Animal Groups: The Importance of Communication
Resume/Abstract :
We investigate the formation and movement of self-organizing collectives of individuals in homogeneous environments. We review a hyperbolic system of conservation laws based on the assumption that the interactions governing movement depend not only on distance between individuals, but also on whether neighbours move towards or away from the reference individual. The inclusion of direction-dependent communication mechanisms significantly enriches the model behavior; the model exhibits classical patterns such as stationary pulses and traveling trains, but also novel patterns such as zigzag pulses, breathers, and feathers. The same enrichment of model behavior is observed when we include direction-dependent communication mechanisms in individual-based models.
Date Heure/Time : 11/25/2011 - 16:00
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., SALLE SH-3420
Conférencier/Speaker : Alex Furman, University of Illinois at Chicago
Titre/Title : Groups with good pedigrees, or superrigidity revisited
Resume/Abstract :
In the 1970s G.A. Margulis proved that certain discrete subgroups (namely lattices) of such Lie groups as SL(3,R) have no linear representations except from the given imbedding. This phenomenon, known as superrigidity, has far reaching applications and has inspired a lot of research in such areas as geometry, dynamics, descriptive set theory, operator algebras etc. We shall try to explain the superrigidity of lattices and related groups by looking at some hidden symmetries (Weyl group) that they inherit from the ambient Lie group. The talk is based on a joint work with Uri Bader.
Date Heure/Time : 11/18/2011 - 16:00
Lieu/Venue : Université de Montréal, Pav. André-Aisenstadt, 2920, chemin de la Tour, SALLE 6214
Conférencier/Speaker : Michael Levitin, University of Reading
Titre/Title : Tricks in Spectral Theory
Resume/Abstract :
The spectra of elliptic boundary value problems for PDEs (for example, a Laplacian acting in a domain in a Euclidean space or on a Riemannian manifold) can be solved analytically only in a small number of trivial cases. In this talk, we survey a number of analytic or geometric tricks and methods which allow one to obtain some a priori information about these spectral problems (in particular, the geometrically motivated eigenvalue estimates) or drastically simplify their numerical study.
Date Heure/Time : 11/11/2011 - 16:00
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Bun Wong, University of California, Riverside
Titre/Title : Domains with non-compact automorphism groups
Resume/Abstract :
The study of automorphism group of a domain in the Euclidean space stands out as one of the major interests of research in various areas like Lie Groups, Differential Geometry, Several Complex Variables, Algebraic Geometry, Topology, etc., The existence of nontrivial automorphisms reflects certain symmetry of the domain, especially when the group is large. In this talk we survey some old and contemporary developments about how to classify the smooth domains with non-compact automorphism groups. Some new results in this direction will be discussed from the viewpoint of a famous classical theorem of Poincare stating that an Euclidean ball is not biholomorphic to a polydisc for complex dimension at least two.
Date Heure/Time : 11/04/2011 - 16:00
Lieu/Venue : Université de Montréal, Pav. André-Aisenstadt, 2920, chemin de la Tour, SALLE 6214
Conférencier/Speaker : Leonid Chekhov , Steklov Mathematical Institute and Concordia University
Titre/Title : Teichmuller spaces of Riemann surfaces with holes and algebras of geodesic functions
Resume/Abstract :
Poincaré uniformized Riemann surfaces of genus g with s>0 holes represented as a quotient of the hyperbolic upper half-plane under the action of a Fuchsian group admit partitions into ideal triangles (with vertices at the absolute). We provide the fat graph description of the corresponding Teichmüller spaces and of closed geodesics on the Riemann surfaces, as well as describe the Poisson structures on the Teichmüller spaces and on the set of geodesic functions. Automorphisms of these structures are generated by mapping class group transformations. Quantizing these structures we obtain quantum geodesic algebras. For the Riemann surfaces with one and two holes, automorphisms of these quantum algebras can be described in terms of a quantum braid-group action on (finite) subsets of quantum geodesic functions. We use the simplest example of the torus with one hole to illustrate the whole construction.
Date Heure/Time : 10/21/2011 - 16:00
Lieu/Venue : UQAM, 200, rue Sherbrooke O. / salle SH-3420
Conférencier/Speaker : Sergey Norin, McGill University
Titre/Title : Divisors on graphs
Resume/Abstract :
Finite graphs can be viewed, in many respects, as discrete analogues of algebraic curves. In this talk, we consider this analogy in the context of linear equivalence of divisors on a graph. We will state a graph theoretic version of the Riemann-Roch theorem and outline its proof. Additionally, we will discuss harmonic morphisms between graphs and connections of our results to tropical geometry. Based on joint work with Matt Baker.
Date Heure/Time : 10/14/2011 - 16:00
Lieu/Venue :
Conférencier/Speaker : Dmitri Burago, Penn State
Titre/Title : ******* COLLOQUE ANNULÉ / CANCELLED *******
Resume/Abstract :
À venir / Coming soon
Date Heure/Time : 09/30/2011 - 16:00
Lieu/Venue : UQAM, 200, rue Sherbrooke Ouest / SALLE SH-3420
Conférencier/Speaker : Jean-Pierre Serre, Collège de France
Titre/Title : Variation with p of the number of solutions mod p of a system of polynomial equations
Resume/Abstract :
À venir / Coming soon
Date Heure/Time : 09/23/2011 - 16:00
Lieu/Venue : Université de Montréal, Pav. André-Aisenstadt, 2920, chemin de la Tour, SALLE 6214
Conférencier/Speaker : Jayce Getz, McGill University
Titre/Title : On Langlands functoriality
Resume/Abstract :
We will give an informal introduction to the Langlands functoriality conjecture. Time permitting, we will discuss established methods (twisted endoscopy) that have proven important special cases of the conjecture, and more recent ideas (comparisons in beyond endoscopy) that can be used to move further.
Date Heure/Time : 09/16/2011 - 16:00
Lieu/Venue : Université de Montréal, Pav. André-Aisenstadt, 2920, chemin de la Tour, SALLE 6214
Conférencier/Speaker : Paul Biran, ETH, Zurich
Titre/Title : Symplectic topology in the large - from Morse to Floer and beyond
Resume/Abstract :
This talk will survey the important role of Morse theory and its generalizations in symplectic topology and Hamiltonian dynamics. We will start from classical Morse theory, then explain an infinite dimensional variant of it called Floer theory and how it revolutionized symplectic topology. Toward the end of the talk we will present current results and new bifurcations of these theories. No previous knowledge of symplectic topology will be assumed.
Date Heure/Time : 09/09/2011 - 16:00
Lieu/Venue : UQAM, 200, rue Sherbrooke O. / salle SH-3420
Conférencier/Speaker : Fedor Nazarov, University of Wisconsin-Madison and Kent State University
Titre/Title : Non-trivial convex bodies with maximal sections of constant volume
Resume/Abstract :
In late 1960's V. Klee asked if a convex body in $R^d$ ($d>2$) whose maximal sections in all directions have the same volume must be a ball. We give a negative answer by constructing a continuous family of bodies of revolution with this property. This is a joint work with D. Ryabogin and A. Zvavitch.
Date Heure/Time : 06/10/2011 - 16:00
Lieu/Venue : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214
Conférencier/Speaker : Claude Viterbo, École Polytechnique
Titre/Title : Symplectic homogenization
Resume/Abstract :
Given a Hamiltonian on $T^n\times R^n$, we shall explain how the sequence of rescaled Hamiltonians, $(\theta,p)\to H(k\theta , p)$, converges, for a suitably defined symplectic metric, as $k$ goes to infinity. We shall then explain some applications, in particular to symplectic topology and invariant measures of dynamical systems.