Recent Advances in Convex Geometry and Geometric Functional Analysis

Convexity is omnipresent in mathematics and the mathematical sciences. During the past ten years, there has been intensive research in convex geometry. Methods and techniques from different fields have been applied and conversely, concepts from convex geometry have been fruitful in other areas (e.g., stochastic geometry and information theory). Much progress has been achieved and new developments have opened up. Many questions were answered, but even more have been raised. 

Two particularly exciting and active directions of research are the Brunn-Minkowski theory of convex bodies and Geometric Functional Analysis. The former concentrates on quantitative properties of geometric invariants on convex bodies, usually with fixed dimension, while the latter aims to provide qualitative estimations on geometric invariants with the dimension becoming large.

The workshop will place special emphasis on those directions. Specifically, we will focus on the following topics: 
The Orlicz-Brunn-Minkowski theory and its dual theory; Affine geometric analysis; Lp Minkowski problems and their duals; Asymptotic geometric analysis.

It is a main goal of the workshop to bring together specialists on these topics, with the aim to apply a variety of techniques to attack some of the open problems mentioned above. Open problem sessions and introductory talks will help to familiarize the different communities present at the workshop with the various topics and problems.