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Friday, February 12, 2016

**Abstract:** The talk will begin by discussing the wellposedness theory of the KdV equation. This theory took a significant step forward in the 90s when Bourgain proved wellposedness on low-regularity Sobolev spaces. These results relied on Fourier restriction norm spaces, which continue to be very important in the study of dispersive PDEs. After this history, I'll discuss some recent work on smoothing and dynamical properties of a coupled KdV-type system.