## Free Probability and Operators

**Date: ** November 17, 2023

**Time: ** 4:00PM - 5:00PM

**Location: ** BLOC 306

**Speaker: **Ryo Toyota, TAMU

**Title: ***Complete Haagerup inequality for Gromov hyperbolic groups*

**Abstract: **In 1978, U Haagerup showed that if f is a function of the free group F_r which is supported on words with length exactly k, then the operator norm of the left regular representation |lambda(f)| is bounded by (k+1) times l^2-norm of f. Now this is called the Haagerup inequality, and its operator valued analogue was proved by Buchholz. In the operator valued case, the above (k+1)-l^2-norms is replaced by different (k+1)-operator norms associated to word decompositions. We will discuss how to generalize it for Gromov hyperbolic groups. This is a joint work with Zhiyuan Yang.