##### Department of Mathematics,

University of California San Diego

****************************

### Math 296 - Graduate Student Colloquium

## Tianyi Zheng

#### UCSD

## How groups grow

##### Abstract:

Given a Cayley graph of a finitely generated group, one can consider its growth function which counts how many elements are there in a ball of radius n on the graph. We will discuss two seminal results in the subject of growth of groups proved in early 1980s: Gromovâ€™s polynomial growth theorem and Grigorchukâ€™s construction of groups of intermediate growth. We will illustrate how random walks on the Cayley graphs can help to study growth.

Host: Jon Novak

### March 14, 2018

### 12:00 PM

### AP&M 6402

****************************