Transport and renormalization via probabilistic Hessian estimates

Vienna Probability Seminar

Probabilistic representations of analytic objects have proven to be a valuable tool in analysis and geometry. I will talk about such representations which lead to sharp control on the Hessians of functions along the heat flow. These results lead to new Lipschitz properties of transport maps in Euclidean and manifold settings, and also show up in renormalization groups techniques.