### Talk by Hoi Nguyen (Ohio State University)

Date and Time: May 29, 10:00 AM in AP&M 6402

Title: On real roots of random Bernoulli polynomials

Abstract:
By using a simple method, we show that a random ∓1 polynomial of degree n does not have double roots with probability tending to one (as n tends to infinity). As a consequence, we deduce that the expected number of real roots is (2/π)(log n) + C + o(1) for some absolute constant C. The method extends to more general coefficient distributions.
(Based on joint work with O. Nguyen and V. Vu)