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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.

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.

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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.

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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 give new applications to the study of hypocoercive estimates for Kolmogorov type operators.

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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.

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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.

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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. Friz and N. Victoir.

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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 course given during the Finnish Summer School in Probability 2012.

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