##### Department of Mathematics,

University of California San Diego

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

### Food For Thought Seminar

## Jason O'Neill

#### UCSD

## The $\epsilon$-net method

##### Abstract:

In this talk, we will explore the problem of the largest singular value of a random sign matrix. We will use the method of $\epsilon$-nets to show that there exists a $C>0$ so that the largest singular value of a random sign matrix of size $n$ is at least $C \sqrt{n}$ with exponentially high probability. While this is a highly combinatorial problem, the method of $\epsilon$-nets could of interest to those in other fields. This talk is based off Tao's book on Random Matrix theory and a recent talk he gave at the 27th Annual PCMI Summer Session on Random Matrices.

### October 30, 2018

### 1:00 PM

### AP&M 7321

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