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Mathematics Colloquium

Adrian Nachman
University of Toronto

Title: A nonlinear Plancherel Theorem with applications to global well-posedness for the Defocusing Davey-Stewartson Equation and to the Calderon Inverse Problem in dimension 2
Date: Friday, September 24, 2021
Place and Time: Zoom, 3:05-3:55 pm


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 background and main ideas for the solution of this problem, as well as for 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.)