A Nonlinear Plancherel Theorem with Applications to Global Well-posedness for a Davey-Stewartson Equation and to the Calderon Inverse Boundary Value Problem

Adrian Nachman (University of Toronto)

Abstract. We consider a well-studied nonlinear Fourier transform in two dimensions for which a proof of the Plancherel theorem had been a challenging open problem.
The talk will explain the background and the main ideas involved in the solution of this problem, as well as in the solution of two other open problems that motivated it: global well-posedness for the defocusing DSII equation in the mass critical case, and global uniqueness for the inverse boundary value problem of Calderon for a class of unbounded conductivities.
Included will be two theorems of independent interest: new estimates for classical fractional integrals, and a new result on boundedness of pseudodifferential operators with non-smooth symbols.
All of this is joint work with Idan Regev and Daniel Tataru.