Functional Inequalities: Geometric Calculus meets Stochastic Analysis

Abstract

Functional inequalities form a unifying theme across a wide spectrum of modern analysis, geometry, and probability. They encode deep geometric and analytic information – for instance through Poincaré, log-Sobolev, transportation, isoperimetric and curvature-dimension inequalities – and serve as crucial tools in the study of Markov semigroups, diffusion processes, metric measure spaces, and geometric flows. The workshop brought together researchers working in geometric analysis, stochastic analysis, and optimal transport in order to promote exchange of ideas and further strengthen the interaction between these rapidly developing fields. Substantial emphasis was placed on non-smooth or singular geometric structures, stochastic dynamics with degeneracies, and new bridges between discrete, fractal, and continuum settings.