S³ seminar : Fourier transforms of polytopes and their role in Number Theory and Combinatorics

Séminaire le 21 Décembre 2017, 11h30 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40
Sinai Robins, (University of Sao Paulo, Sao Paulo, Brasil and Brown University, Providence, USA)

We introduce the topic of the Fourier transform of a Euclidean polytope, first by examples and then by more general formulations.  Then we point out how we can use this transform (and the frequency space) to analyze the following problems:
1.  Compute lattice point enumeration formulas for polytopes
2.  Relate the transforms of polytopes to tilings of Euclidean space by translations of a polytope

We will give a flavor of how such applications arise, and we point to some conjectures and applications.