PSU Mathematics Department - Meeting Details

For more information about this meeting, contact Sergei Tabachnikov, Flossie Dunlop.

Abstract:
Title:	Inverse problems in Arithmetic Combinatorics
Seminar:	MASS Colloquium
Speaker:	Alexander Razborov, Institute for Advanced Study
Arithmetic Combinatorics studies behavior of subsets of algebraic structures under their operations. In inverse problems we know something about this behaviour; a typical assumption would indicate that the subset A in question expands under those operations much less than expected. And we want to derive some conclusions about the internal structure of A. It turns out that even the most basic questions of this sort about the simplest structures like Z or F_p lead to either very deep and difficult theorems or to widely open important questions, and I hope to discuss some of them in my talk. It is worth noting that in recent years many of these ideas and results have found rather unexpected applications in many different areas, such as Harmonic Analysis or Theoretical Computer Science.