Recent work on the Kakeya conjecture

A Besicovitch set is a subset of R^n which contains a unit line segment in each direction; the Kakeya conjecture states that such sets must have Minkowski and Hausdorff dimension n. This turns out to be relevant to a number of open problems in analysis, including the restriction conjecture and the Bochner-Riesz conjecture.

This talk will begin with a non-technical discussion of the Kakeya conjecture and of its status prior to 1998. I will then report on the recent results of Bourgain and Katz-Laba-Tao, which use a new combinatorial approach to the problem and improve on the best previous results due to Wolff.

Refreshments will be served in Math Annex Room 1115, 3:15 p.m.