Seminar Physique Mathématique -- On symmetries of stochastic differential equations

10/20/2015 - 15:30
10/20/2015 - 16:30
Speaker: 
Roman Kozlov (Department of Business and Management Science, Norwegian School of Economics)
Location: 
CRM, UdeM, Pavillon André-Aisenstadt, 2920, ch. de la Tour, Salle 4336
Abstract: 

Recently there appeared applications of Lie group theory to stochastic differential equations (SDEs). Different approaches were suggested. Here we deal with infinitesimal Lie group transformations which leave the form of SDEs and the frame- work of Itô calculus invariant. There will be reviewed results concerning with Lie point symmetries of 1. scalar stochastic differential equations with one-dimensional Brownian motion: the admitted symmetry group is at most three-dimensional; 2. systems of stochastic differential equations with diffusion matrices of full rank: the admitted symmetry group of a system of n SDEs is at most (n+2)-dimensional; 3. scalar stochastic diÆerential equation of order n>=3 with one-dimensional Brownian motion: the admitted symmetry group is at most (n+2)-dimensional. Finally, we consider the relation between symmetries of SDEs and symmetries of the associated Fokker-Planck equation. The relation between first integrals of SDEs and symmetries of the associated Fokker-Planck equation is also mentioned.

Last edited by on Mon, 10/19/2015 - 16:08

Presenting a Category Modulo a Rewriting System

10/20/2015 - 14:30
10/20/2015 - 16:00
Speaker: 
Florence Clerc (McGill University)
Location: 
Burnside Hall, Rm. 920 (McGill University)
Abstract: 

Presentations of categories is a useful tool to describe categories by the means of generators for objects and morphisms and relations on morphisms. However problems arise when trying to generalize this construction when objects are considered modulo an equivalence. Three different constructions can be used to describe such generalization : localization, quotient and considering only normal forms with respect to a certain rewriting system.

I will present some work done in collaboration with S.Mimram and P.L.Curien. We assume two kinds of hypotheses, namely convergence and cylinder property (which is some higher-dimensional convergence). Under these assumptions, we prove that there is an equivalence of categories between the quotient and the localization, and an isomorphism of categories between the quotient and the category of normal forms.

Last edited by on Mon, 10/19/2015 - 16:05

Geometric Analysis Seminar -- Flow by powers of the Gauss curvature

10/28/2015 - 13:30
10/28/2015 - 14:30
Speaker: 
Pengfei Guan (McGill University)
Location: 
Burnside Hall, Rm. 920 (McGill University)
Abstract: 

We discuss a joint work with Ben Andrews and Le i Ni on the Gauss curvature flow by powers. We prove that convex hypersurfaces in ${\mathbb R}^{n+1}$ contracting under the flow by any power $\alpha>\frac{1}{n+2}$ of the Gauss curvature converge (after rescaling to fixed volume) to a limit which is a smooth, uniformly convex self-similar contracting solution of the flow. Under additional central symmetry of the initial body we prove that the limit is the round sphere.

 

 

Last edited by on Mon, 10/19/2015 - 13:59

Geometric Group Theory Seminar -- The Stable Boundaries of CAT(0) Groups

10/21/2015 - 15:00
10/21/2015 - 16:00
Speaker: 
Dooheon Lee (New York University)
Location: 
Burnside Hall, Rm. 920 (McGill University)
Abstract: 

It is well-known that Gromov-hyperbolic groups have well-defined boundaries. As demonstrated by Croke and Kleiner, however, the same can not be said for CAT(0) groups. To remedy this issue, Charney and Sultan defined a new type of boundary, called the contracting boundary, for CAT(0) groups. Except Gromov-hyperbolic cases, however, the contracting boundaries of CAT(0) groups are not topologically generic. To be precise, suppose G acts on a CAT(0) space X and G is not Gromov-hyperbolic, then the contracting boundary of X is of first Baire category in \partial X . In this paper, we introduce stable boundaries for CAT(0) groups, which coincide with the usual boundary in the cases of Gromov-hyperbolic groups. We provide a sufficient condition for stable boundaries of CAT(0) groups to be topologically generic in the above sense. In particular, we show that the stable boundaries of right angled Artin groups, Coxeter groups, and CAT(0) groups with codimension one free Abelian subgroups are generic when they have rank one axial isometries.

Last edited by on Mon, 10/19/2015 - 13:51

Applied Mathematics Seminar -- Heart Wall Myofibers are Arranged in Minimal Surfaces

10/19/2015 - 15:00
10/19/2015 - 16:00
Speaker: 
Kaleem Siddiqi (McGill University)
Location: 
Burnside Hall, Rm. 920 (McGill University)
Abstract: 
Heart wall myofibers wind as helices around the ventricles, strengthening them in a manner analogous to the reinforcement of concrete cylindrical columns by spiral steel cables. A multitude of such fibers, arranged smoothly and regularly, contract and relax as an integrated functional unit as the heart beats. To orchestrate this, fiber tangling must be avoided while pumping should be efficient. Current models of myofiber orientation across the heart wall suggest groupings into sheets or bands, but the precise geometry of bundles of myofibers is unknown. Here we show that this arrangement takes the form of a special minimal surface, the generalized helicoid, closing the gap between individual myofibers and their collective wall structure. The model holds across species, with a smooth variation in its three curvature parameters within the myocardial wall providing tight fits to diffusion magnetic resonance images from the rat, the dog and the human. Mathematically it explains how myofibers are bundled in the heart wall while economizing fiber length and optimizing ventricular ejection volume as they contract. The generalized helicoid provides a novel foundation for analyzing the fibrous composite of the heart wall and should therefore find applications in heart tissue engineering and in the study of heart muscle diseases. 
Last edited by on Mon, 10/19/2015 - 13:29

Colloque des sciences mathématiques du Québec -- Coxeter Groups and Quiver Representations

10/09/2015 - 16:00
10/09/2015 - 17:00
Speaker: 
Hugh Thomas (UQAM)
Location: 
UQAM - Pavillon Sherbrooke, ** Salle SH-2420 **
Last edited by on Thu, 10/08/2015 - 10:27

Geometry-Topology -- Stable classification of 4-manifolds with 3-manifold fundamental groups

10/09/2015 - 14:00
10/09/2015 - 15:00
Speaker: 
Daniel Kasprowski (Max Plank Institute for Mathematics)
Location: 
PK-2265, Pavillon Président-Kennedy, UQAM
Last edited by on Thu, 10/08/2015 - 10:25

Seminar LACIM -- Compter les idéaux de $F_q[x,y,x^{-1},y^{-1}]$ donne un q-analogue de la fonction "somme des diviseurs de n"

10/09/2015 - 13:30
10/09/2015 - 14:30
Speaker: 
Christophe Reutenauer (UQAM)
Location: 
201, av. du Président-Kennedy, LOCAL PK-4324, Montréal (Qc) H2X 3Y7
Abstract: 
Last edited by on Thu, 10/08/2015 - 10:23

Geometry-Topology -- Regularizing infinite sums of zeta-determinants

10/09/2015 - 11:00
10/09/2015 - 12:00
Speaker: 
Boris Vertman (Universität Bonn)
Location: 
PK-5115, Pavillon Président-Kennedy, UQAM
Last edited by on Thu, 10/08/2015 - 10:09

Minicourse I - Introduction to topological recursion : Topological recursion: Moduli spaces and Gromov-Witten Theory

10/08/2015 - 16:00
10/08/2015 - 17:00
Speaker: 
Bertrand Eynard (CPT, CEA Saclay)
Location: 
Concordia University, Math Help Center, room 912.00 / Library Building, 1400 de Maisonneuve Blvd. West, Montréal
Abstract: 

Moduli spaces and Gromov-Witten theory.

Last edited by on Thu, 10/08/2015 - 10:07