Alex Iosevich (Rochester)
Multi-linear operators, geometric measure
theory and combinatorics
Abstract: Sobolev bounds for classical Fourier integral operators have
been used with great success over the years in partial differential
equations, geometry and many other areas. In this talk we shall
establish some simple bounds for multi-linear analogs of these
operators and we shall deduce some interesting consequences for a
diverse set of problems in classical harmonic analysis, Falconer-Erd\H
os type problems in geometric measure theory and combinatorics, and
best constants for Sobolev type inequalities.