### Tuesday, November 15, 2016 (3:00 p.m. in Yost 306)

**Title:** Self-similarity in the eigenvalues of random unitary matrices

**Speaker:** Mark Meckes (Associate Professor, MAMS Department, Case Western Reserve University)

**Abstract:** In a statistical study of the observed relationship between eigenvalues of large random unitary matrices and zeros of the Riemann zeta function, Coram and Diaconis proposed a “self-similarity” phenomenon for random unitary eigenvalues. Roughly, they suggested that the eigenvalues of an n x n random matrix should be statistically indistinguishable from half the eigenvalues of a 2n x 2n random matrix, with suitable rescaling. I will present a rigorous result along these lines, joint with Elizabeth Meckes, and build up some of the general machinery needed for the proof.