##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Sam Mellick

#### McGill University

## Vanishing of rank gradient for lattices in higher rank Lie groups via cost

##### Abstract:

In 2016 Abert, Gelander, and Nikolov made what they called a provocative conjecture: for lattices in higher-rank simple Lie groups, the minimum size of a generating set (rank) is sublinear in the volume. I will discuss our solution to this conjecture. It is a corollary of our main result, where we establish "fixed price one" for a more general class of "higher rank" groups. No familiarity of fixed price or cost is required for the talk. Joint work with Mikolaj Fraczyk and Amanda Wilkens.

Host: Brandon Seward

### May 11, 2023

### 10:00 AM

APM 7218 and Zoom ID 967 4109 3409

Email an organizer for the password

Research Areas

Ergodic Theory and Dynamical Systems****************************