##### Department of Mathematics,

University of California San Diego

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### Math 243 - Functional Analysis

## Brian Hall

#### University of Notre Dame

## Eigenvalues of random matrices in the general linear group

##### Abstract:

I will consider random matrices in the general linear group GL(N;C) distributed according to a heat kernel measure. This may also be described as the distribution of Brownian motion in GL(N;C) starting at the identity. Numerically, the eigenvalues appear to cluster into a certain domain $\Sigma_t$ as $N$ tends to infinity. A natural candidate for the limiting eigenvalue distribution is the â€œBrown measureâ€ of the limiting object, which is Bianeâ€™s ``free multiplicative Brownian motion.'' I will describe recent work with Driver and Kemp in which we compute this Brown measure. The talk will be self contained and will have lots of pictures.

Host: Todd Kemp

### February 5, 2019

### 10:00 AM

### AP&M 6402

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