3:30 p.m., Friday
Professor Izabella Laba
Department of Mathematics
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.