Gyula Károlyi: The Coefficient Lemma and some of its applications

Abstract: There are several problems in addditive combinatorics,
which can be solved using the polynomial method, with
some kind of application of the Combinatorial
Nullstellensatz. This tipically involves the
computation of a leading coefficient of some
multivariate polynomial designed for the problem.
This sometimes presents a difficult combinatorial
task. In many cases the so-called Coefficient Lemma
is a useful tool to simplify the involved combinatorics.
It can also be used to compute Selberg-type integrals
that are important in statistical mechanics.
In this talk I will review some typical applications.

For Zoom access please contact Andras Biro (biro.andras[a]renyi.hu).