Title： Application of waist inequality to entropy and mean dimension
Speaker: Professor Masaki Tsukamoto, Department of Mathematics, Kyoto University, Japan
Abstract： Waist inequality is a deep geometric-topological inequality introduced by Gromov. It states that every continuous map from the sphere to the Euclidean space (of lower dimension) has a large fiber. This inequality and its variants have interesting applications in several areas, most notably in convex geometry and combinatorics.
The purpose of this talk is to explain its new applications in dynamical systems theory.
The prototype of our result is as follows: Let $X$ be the full-shift on the alphabet the unit square, and let $Y$ be the full-shift on the alphabet the unit interval.
Then every equivariant continuous map from $X$ to $Y$ has a fiber of infinite entropy.
This talk is based on a joint work with Ruxi Shi.