New York Number Theory Seminar
March 20, 2003, 3:30 PM in Room 5417
- Speaker:
- Mel Nathanson, Lehman College (CUNY)
- Title:
- Additive number theory and the Hausdorff dimension of Kakeya sets
(apres Bourgain, Katz, and Tao)
- Abstract:
- Recent work in harmonic analysis has connected the problem of
computing the Hausdorff and Minkowski dimensions of Kakeya sets in
Euclidean space to combinatorial problems in additive number theory,
and has also introduced the problem of computing the cardinalities of
Kakeya sets in vector spaces over finite fields. This is directly
related to the Erdos-Szemeredi problem on the number of sums and
products of a finite set of integers. We shall review some of recent
work by Jean Bourgain, Nets Hawk Katz, and Terence Tao. Preprints of
their papers are posted on www.arXiv.org.