My research explores how stochastic methods can be used to understand geometric and analytic structures. I focus on using techniques from diffusion processes, particularly heat kernels, to derive functional inequalities on Lie groups, manifolds, and fractal spaces. These inequalities often offer fresh perspectives, allowing us to define novel notions of curvature bounds. Additionally, I am interested in calculating the exact probability distributions for functionals arising from Brownian motion on homogeneous spaces or matrix spaces.
I have been teaching a variety of undergraduate, graduate and topics courses over the years. Some of the lecture notes are posted on my blog
https://fabricebaudoin.blog
