Ohio State is in the process of revising websites and program materials to accurately reflect compliance with the law. While this work occurs, language referencing protected class status or other activities prohibited by Ohio Senate Bill 1 may still appear in some places. However, all programs and activities are being administered in compliance with federal and state law.

Combinatorics Seminar - Rob Morris

Combinatorics Seminar
October 22, 2020
10:20 am - 11:15 am
Zoom

Title: Flat Littlewood Polynomials Exist
 
Speaker: Rob Morris - IMPA
 
Abstract: A polynomial $P(z) = \sum_{k=0}^n \eps_k z^k$ is a Littlewood polynomial if $\eps_k \in \{-1,1\}$ for all $k$. Littlewood proved many beautiful theorems about these polynomials over his long life, and in his 1968 monograph he stated several influential conjectures about them. One of the most famous of these was inspired by a question of Erd\H{o}s, who asked in 1957 whether there exist “flat” Littlewood polynomials of degree $n$, that is, such that
 
 $$\delta\sqrt{n} \le |P(z)| \le \Delta\sqrt{n}$$
 
 for all $z \in \mathbb{C}$ with $|z|=1$, for some absolute constants $\Delta > \delta > 0$. In this talk we will describe a proof that flat Littlewood polynomials of degree $n$ exist for all $n \ge 2$. The proof is entirely combinatorial, and uses probabilistic ideas from discrepancy theory.
 
 Joint work with Paul Balister, Béla Bollobás, Julian Sahasrabudhe and Marius Tiba. 

Events Filters: