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.