Abstract

The conjecture broadly asserts that small data should yield global solutions for 1D defocusing dispersive flows with cubic nonlinearities, in both semilinear and quasilinear settings. The aim of the talk will be to describe the framework of this conjecture, some very recent results in this direction, as well as extensions to higher dimensions. This is joint work with Mihaela Ifrim.

Short Bio

Daniel Tataru, currently a Professor at UC Berkeley since 2001, rose from Assistant Professor (1992-1996) to Professor (1999-2001) at Northwestern University, with a brief stint at IAS/Princeton University from 1995 to 1997. He earned his Ph.D. from the University of Virginia in 1992. He demonstrated exceptional aptitude in mathematics from an early age, earning top honors in International Mathematics Olympiads.

His early work focused on Hamilton-Jacobi equations in Banach spaces. Under the guidance of advisors Irena Lasiecka and Roberto Triggiani, his graduate research delved into Carleman estimates and their applications in unique continuation and control theory. Daniel’s current research interests revolve around nonlinear dispersive equations, with implications spanning harmonic analysis, geometry, theoretical physics, and fluid dynamics. His contributions have been acknowledged with numerous accolades, including the 2001 Bôcher Prize from the American Mathematical Society, honorary membership at the Simion Stoilow Institute of Mathematics in Bucharest, and the 2015 Humboldt Research Award. He’s been a Simons Investigator since 2013 and a fellow of the American Academy for Arts and Sciences since 2014, as well as a fellow of the European Academy of Sciences since 2019.

Outside of mathematics, Daniel enjoys soccer, hiking, mountain biking, and is an avid bridge player. For further info visit his webpage.

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