Some connections between harmonic analysis and combinatorial geometry

Thomas Wolff
California Institute of Technology

I will discuss some situations where techniques from combinatorics can be used to prove L^p estimates in harmonic analysis or conversely estimates familiar in L^p harmonic analysis can be used in connection with geometrical problems - more specifically, aspects of recent work on the Kakeya problem, and joint work with M. Kolountzakis on the so-called Steinhaus tiling problem.