Category Archives: Lecture Notes

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.  

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 … Continue reading →

Download   These notes are the basis of a course given at the Institut Henri Poincare in September 2014. We survey some recent results related to the geometric analysis of hypoelliptic diffusion operators on totally geodesic Riemannian foliations. We also … Continue reading →

Download   In those lecture notes, we review some applications of heat semigroups methods in Riemannian and sub-Riemannian geometry. The notes contain parts of courses taught at Purdue University, Institut Henri Poincaré, Levico Summer School and Tata Institute.

Download   Those are the notes corresponding to my book on stochastic flows. Most of them were written in 2003 during my stay as a postdoc at the Technical University of Vienna.  

Download   Those are the notes of a course on rough paths theory taught at Purdue University in Spring 2013. We develop the theory according to its founder Terry Lyons’ point of view and rely on the book by P. … Continue reading →

Download   Those are lecture notes on stochastic differential equations driven by fractional Brownian motions. It only deals with the case , so that the equations are understood in the sense of Young’s integration. Those notes correspond to a mini … Continue reading →

Download Those are the lecture notes of the stochastic calculus course I have been teaching at the University of Toulouse (2003-2008) and then at Purdue University. Some parts of this book grew out of the lectures posted on this blog. … Continue reading →

Download During my Phd thesis (completed in 2002 under the supervision of Marc Yor) I worked on applying stochastic calculus to mathematical finance. I quit doing research on mathematical finance soon after the thesis but was invited to deliver lectures … Continue reading →