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.
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September 3, 2020, TBA (TBA)
September 10, 2020,
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.