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:
https://nam10.safelinks.protection.outlook.com/?url=http%3A%2F%2Fcalendar.uconn.edu%2F2019%2Fmonth%2F11%2F376%2F&data=02%7C01%7Cuconn_probability-l%40listserv.uconn.edu%7Cd8ca055733eb421930fd08d7b15a6d44%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C637172874245514015&sdata=bUAahk%2BdQ9gDEQqhbrdrt6mamD1IXP05S8cwvQaOaNo%3D&reserved=0.
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
