Marta Sanz-Solé (Barcelone) 

Abstract : The lecture will be on Gaussian Malliavin calculus and some of its applications. In the first part, I will give an elementary introduction focussing on the probabilistic motivations, the underlying ideas, and some of its more popular applications. In the second part, we will concentrate on applications to stochastic partial differential equations. Some recent results and open problems will be presented.

Coffee break

Dynamical system on the torus."

Abstract : One of the aims of Ergodic Geometry is to describe the statistical behavior of the trajectories of a smooth dynamical system. Even for the action of unimodular integral matrices on the 2-torus this behavior can be quite chaotic. With JF Quint, we focus on a very concrete question. Let A and B be two such matrices  spanning a non-solvable group. Let x be an irrational point on the 2-torus. We toss A or B, apply it to x, get another irrational point y, do it again to y, get a point z, and again. We check that this random trajectory is equidistributed on the torus. Moreover this phenomenon is quite general on any finite volume homogeneous space.

Dinner at the Dorigny University Restaurant. If you are interested in participating, please register before February 23 by sending me an email, do not forget to indicate how many people you will be in case you register in groupe/couple. Thank you.