EVENT DETAILS AND ABSTRACT

Title: Hypercontractivity, Convexity, and Lower Deviations
Speaker: Petros Valettas
Speaker Info: University of Missouri
Brief Description:
Special Note:
Abstract:

The concentration of measure phenomenon is an indispensable tool in the study of high-dimensional phenomena. Nonetheless, there exist several key situations that yields suboptimal results. We will discuss how this probabilistic principle admits stronger forms in the presence of convexity and how the local version of them can be combined with a blend of analytic, combinatorial, and topological methods in order to obtain sharp small ball probabilities for norms in high dimensions. Time permitting we will present applications in asymptotic geometric analysis. Based on joint work with Grigoris Paouris and Konstantin Tikhomirov.