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Varun Jog, University of Wisconsin-Madison, Reverse Euclidean and Gaussian isoperimetric inequalities for parallel sets with applications
September 14, 2020 | 3:00 pm - 4:00 pm EDT
The r-parallel set of a measurable set A is the set of all points whose distance from A is at most r. In this talk, we discuss some recent results that establish upper bounds on the Euclidean and Gaussian surface areas of r-parallel sets. We also discuss a reverse form of the Brunn-Minkowski inequality for r-parallel sets, and as an aside a reverse entropy power inequality for Gaussian-smoothed random variables. We will conclude by presenting applications of our results to some problems of interest in theoretical machine learning.
Host: Paata Ivanisvili pivanis@ncsu.edu