Thursdays in 901 Van Vleck Hall at 2:30 PM, unless otherwise noted. We usually end for questions at 3:20 PM.
IMPORTANT: In Fall 2020 the seminar is being run online.
If you would like to sign up for the email list to receive seminar announcements then please send an email to firstname.lastname@example.org
September 15, 2020, Boris Hanin (Princeton and Texas A&M)
September 23, 2020, Neil O'Connell (Dublin)
October 1, 2020, Marcus Michelen, UIC
Title: Roots of random polynomials near the unit circle
Abstract: It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe.
October 8, 2020, Subhabrata Sen, Harvard
November 12, 2020, Alexander Dunlap, NYU Courant Institute