Asymptotic and classical convexity theories are nowadays intertwined. Results of one field are used in the other with numerous applications. Among recent important developments are results of a geometric-probabilistic flavor on the volume distribution in convex bodies, central limit theorems for convex bodies and others, with close links to geometric inequalities and optimal transport. In fact, the geometric theory of convexity is extended to a larger category of (log-concave) measures. This point of view introduces, in particular, functional versions for many geometric inequalities, and also leads to solutions of some central problems of geometry and analysis.

This workshop is a result of the rapid development seen in recent years in the fields of Convexity and Asymptotic Geometric Analysis. The talks will survey the current state of the fields with focus on the latest advances and the remaining challenges.