# Topological (Geometric) Combinatorics via finite Fourier analysis

## Steven Simon, Wellesley College

## September 29, 2015

Methods of equivariant topology have been successfully applied in
recent years to a variety of problems in geometric combinatorics,
especially to those concerning measure equipartitions (generalizations
of the ham sandwich-theorem: any $d$ masses in $\mathbb{R}^d$ can be
bisected by a single hyperplane) and point partitions of a
Tverberg-type (generalizations of Radon's theorem: any $d+2$ points in
$\mathbb{R}^d$ can be partitioned into two sets with overlapping
convex hulls). Reformulating these problems and their topological
reductions in terms of harmonic analysis on finite groups, we will
show how a variety of both classical and new partition theorems can
be obtained as the annihilation of prescribed Fourier transforms.