Title: Flat Littlewood Polynomials Exist
| Speaker: | Robert Morris |
| Affliation: | IMPA (Instituto de Matemática Pura e Aplicada) |
| Zoom: | Please email Emma Watson |
Abstract:
In a Littlewood polynomial, all coefficients are either 1 or -1. 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 Erdos, who asked in 1957 whether there exist "flat" Littlewood polynomials of degree n, that is, with |P(z)| of order n^{1/2} for all (complex) z with |z| = 1.
In
this
talk
we
will
describe
a
proof
that flat
Littlewood
polynomials
of
degree
n
exist
for
all
n
>
1.
The
proof
is
entirely
combinatorial,
and
uses
probabilistic
ideas
from
discrepancy
theory.
Joint
work
with Paul
Balister,
Béla
Bollobás,
Julian
Sahasrabudhe
and
Marius
Tiba.