SILO



The weekly SILO Seminar Series is made possible through the generous support of the 3M Company and its Advanced Technology Group

3M

with additional support from the Analytics Group of the Northwestern Mutual Life Insurance Company

Northwestern Mutual

Geometric tools in information theory

Varun Jog, Assistant Professor, Department of Electrical and Computer Engineering, University of Wisconsin-Madison

Date and Time: Sep 21, 2016 (12:30 PM)
Location: Orchard room (3280) at the Wisconsin Institute for Discovery Building

Abstract:

Video: https://vimeo.com/184352560

Concepts in geometry often have parallels in information theory; for example, volume and entropy, surface area and Fisher information, sphere-packing and channel coding, and Euclidean balls and Gaussian distributions, to name a few. These similarities provide a simple way to posit theorems in one area by translating the corresponding theorems in the other. However, the analogy does not extended fully, and the proof techniques often do not carry over without substantial modification. In this talk, I will try to bridge this gap by interpreting information-theoretic problems through the lens of high-dimensional geometry. This approach makes it possible to create new mathematical tools in information theory using existing tools in geometry. I will focus on two applications of these tools: analyzing the Shannon capacity of energy-harvesting channels, and obtaining a generalization of differential entropy for log-concave distributions. I will also describe some open problems and conjectures related to this line of work.