https://www.math.toronto.edu/cms/people/faculty/nachman-adrian/
Thu, April 23, 2020, 9:00-10:00 am PST via Zoom
Title: 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 recent 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 Calderon 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.)