Windings of unitary Brownian motion

Here is the talk I gave at the very nice conference Stochastic differential geometry and mathematical physics which virtually took place from june 7th to june 11th 2021.

At the end of the talk, there is a discussion by Franck Gabriel.

Posted in Uncategorized | Leave a comment

Heat flow and sets of finite perimeter (AMS invited address)

Here is the video of my invited AMS address given Sunday, April 18 2021, during the AMS sectional meeting 1166.

Posted in Uncategorized | Leave a comment

Asymptotic windings of unitary Brownian motions

Posted in Uncategorized | Leave a comment

Log-Sobolev inequalities

Survey talk about log-Sobolev-inequalities

Posted in Uncategorized | Leave a comment

Heat flow and sets of finite perimeter

I will be giving an invited address at the Spring Central Sectional Meeting on Sunday, April 18, 11.45am US Central time.

The main topic of the address will be the study of isoperimetric inequalities and sets of finite perimeter using heat kernel techniques. The first part of the talk will be elementary with an historical perspective and then I will be presenting more recent research directions. Here is a more detailed abstract.

Posted in Uncategorized | Leave a comment

Fractional Gaussian fields on fractals

Posted in Uncategorized | Leave a comment

H-type manifolds

H-type manifolds are natural structures that arise as generalizations of H-type groups. Below is a talk I gave on that topic that took place during the conference : Sub-Riemannian Geometry and Interactions Paris, September 7–11, 2020.

Posted in Uncategorized | Leave a comment

Einstein manifolds

This Fall, I am teaching a graduate course on Einstein manifolds.

In this course we will study some topics in Riemannian and pseudo-Riemannian geometry. We will mostly focus on Ricci curvature and its applications. The course will start with basics about Riemannian and pseudo-Riemannian geometry. We will assume familiarity with differential manifolds and basic calculus on them.

We will cover the following topics:


Linear connections on vector bundles: Torsion, Curvature, Bianchi identities
Riemannian and pseudo-Riemannian manifolds
Get the feel of Ricci curvature: Volume comparison theorems, Bonnet-Myers theorem
Ricci curvature as a PDE
Einstein manifolds and topology
Homogeneous Riemannian manifolds
Kahler and Calabi-Yau manifolds
Quaternion-Kahler manifolds

The main reference for the class will be: A.L. Besse: Einstein manifolds, Springer, 1987.

Due to the Covid pandemic those lectures are online and the videos are publically posted on a dedicated webpage.

Posted in Uncategorized | Leave a comment

Lecture notes: Dirichlet spaces

Download

 

Those lecture notes are associated to a course I taught at the University of Connecticut in Spring 2019. The focus is on the theory of Dirichlet spaces and heat kernels in metric measure spaces.

 

Posted in Lecture Notes | Leave a comment

Lecture Notes: Brownian Chen series and Gauss-Bonnet-Chern theorem

Download

 

The purpose of these notes is to provide  a new probabilistic approach to the Gauss-Bonnet-Chern theorem (and more generally to index theory). They correspond to a five hours course given at a Spring school in France (Mons) in  June 2009.

Posted in Lecture Notes | Leave a comment