Dear all,
We have two talks today in the Analysis and Probability seminar. The first speaker is Paul Bourgade from NYU at 1:30PM in MONT 313. The title of his talk is "Branching processes in random matrix theory and analytic number theory". The second speaker is Mariana Smit Vega Garcia from Western Washington University at 3:30PM in MONT 214 (Note room). The title of her talk is "On a Bernoulli-Type Overdetermined Free Boundary Problem". You can find both abstracts below.
You can find information about future A/P talks here: http://calendar.uconn.edu/2019/month/11/376/.
Title: Branching processes in random matrix theory and analytic number theory
Abstract: Fyodorov, Hiary and Keating have conjectured that the maximum of the characteristic polynomial of random matrices behaves like extremes of log-correlated Gaussian fields. This allowed them to predict the size of local maxima of L-function along the critical axis. I will explain the origins of this conjecture and some rigorous understanding, for unitary random matrices and the Riemann zeta function, relying on branching structures.
Title: On a Bernoulli-Type Overdetermined Free Boundary Problem
Abstract: Abstract: We study a Bernoulli-type free boundary problem in the context of A-harmonic PDEs. In particular, we show that if K is a bounded convex set satisfying the interior ball condition and 𝑐>0 is a given constant, then there exists a unique convex domain U containing K and a function u which is A-harmonic in 𝑈∖𝐾, has continuous boundary values 1 on ∂𝐾 and 0 on ∂𝑈, such that |∇𝑢|=𝑐 on ∂𝑈. Moreover, ∂𝑈 is 𝐶1,𝛾, for some 𝛾>0, and it is smooth provided A is smooth in ℝ𝑛∖{0}.
- Sean