A nonlinear Plancherel Theorem with applications to global well-posedness for the Defocusing Davey-Stewartson Equation and to the Calderón Inverse Problem in dimension 2

Abstract: I’ll describe a well-studied nonlinear Fourier transform in two dimensions for which a proof of the Plancherel theorem had been a challenging open problem. I’ll sketch out the main ideas of the solution of this problem, as well as the solution of two other 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 Calderón for a class of unbounded conductivities. On the way, there will also be new estimates for classical fractional integrals, and a new result on L^2 boundedness of pseudodifferential operators with non-smooth symbols. (This is joint work with Idan Regev and Daniel Tataru.)

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine