## Department Colloquium

### Monday, February 12th, 2018

**Time:** 4:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Brad Rodgers, University of Michigan

**Title:** Some Applications of Random Matrix Theory to Analytic Number Theory

**Abstract: **In this talk I'll survey some of the ways that ideas originating from the study of random matrices have had an impact on analytic number theory. I hope to discuss in particular: 1) the statistical spacing of zeros of the Riemann zeta function, and what this spacing has to say about arithmetic, 2) a resolution of conjectures of Saari and Montgomery about the distribution of Rudin-Shapiro polynomials, using a connection to random walks on compact groups, and 3) recent work on the de Bruijn-Newman constant; de Bruijn showed that the Riemann hypothesis is equivalent to the claim that this constant is less than or equal to 0, and I will describe recent work showing the constant is greater than or equal to 0, conrming a conjecture of Newman. This includes joint work with J. Keating, E. Roditty-Gershon, and Z. Rudnick; and with T. Tao.

**Brad Rodgers (University of Michigan):** Brad Rodgers obtained his Ph.D. in Mathematics from the University of California, Los Angeles in 2013 under the supervision of Terence Tao. From 2013 to 2015 he held a postdoctoral position at the Institut fur Mathematik at the Universitat Zurich. Since 2015, he is a Postdoc Assistant Professor at the University of Michigan. Dr. Rodgers's awards include the AMS-Simons Travel Grant (2013-2016) and a NSF research grant (2017-2020). His research interests include random matrix theory, analytic number theory. In particular, he focuses on the interaction of these disciplines with analysis, probability, and combinatorics.