# On a problem of J.E. Littlewood on flat polynomials

• Julian Sahasrabudhe (University of Cambridge)
• Wednesday 16 October 2019, 13:45-14:45
• MR5, CMS.

A polynomial is said to be a Littlewood polynomial if all of its coefficients are either +1 or -1. Erdos, in 1957, asked how `flat’ such polynomials can be on the unit circle. In particular, he asked if there exist infinitely many Littlewood polynomials for which $c_1 \leq \frac{\max_{|z|=1} |f(z)|}{\min_{|z|=1 } |f(z)| } \leq c_2,$ where $c_1,c_2 >0$ are absolute constants. Later, in 1966, Littlewood conjectured that such polynomials should indeed exist.

In this talk I will discuss how combinatorial and probabilistic ideas can be used to resolve this conjecture. This talk is based on joint work with Paul Balister, Bela Bollobas, Rob Morris and Marius Tiba.

This talk is part of the Discrete Analysis Seminar series.