New York Number Theory Seminar
February 6, 2003, 3:30 PM in Room 5417
- Speaker:
- Matt DeVos, Princeton University
- Title:
- A solution to Kneser's critical problem
- Abstract:
- In 1953 Martin Kneser proved an important addition theorem which
gives a natural lower bound on |A+B| for any pair A,B of finite
subsets of an (additive) ablelian group. Three years later he posed
the problem of characterizing those pairs A,B for which |A+B| < |A| +
|B|. Such pairs are now called critical. We have recently proved a
structure theorem which resolves Kneser's problem. It shows that
every critical pair has a recursive structure based on arithmetic
progressions and two other configurations. The goal of this talk is
to describe the structure of critical pairs and to sketch the proof of
this theorem.