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.

# Seminar Physique Mathématique -- On symmetries of stochastic differential equations

# Presenting a Category Modulo a Rewriting System

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.

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

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.

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

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 acts on a CAT(0) space and is not Gromov-hyperbolic, then the contracting boundary of is of first Baire category in . 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.

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

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

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

# 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"

Web site : __http://www.lacim.uqam.ca__

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

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

Moduli spaces and Gromov-Witten theory.