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Math Colloquium
Brad Rodgers
Univ. of Michigan
Title: The distribution of Rudin-Shapiro polynomials and random walks on compact groups

Abstract: Is it possible to find trigonometric polynomials with all coefficients 1 or -1 which stay essentially constant in magnitude? A precise version of this question was first asked by J.E. Littlewood in the 1950s and remains unresolved. The Rudin-Shapiro polynomials are a special sequence of polynomials first studied to shed light on this problem. In this talk I discuss properties of these polynomials, with a focus on some conjectures of B. Saffari and H. Montgomery regarding their limiting distribution. I will describe work resolving these conjectures, which makes use of a surprising connection to random walks on compact groups.

Date: Monday, December 11, 2017
Time: 4:30 pm
Location: Wean Hall 8220
Submitted by:  Bohman
Note: Refreshments at 4:00 pm, Wean Hall 6220.