The small data global well-posedness conjecture for 1D defocusing dispersive flows

Thời gian: 08:30 đến 10:30 Ngày 05/03/2024

Địa điểm: Vietnam Institute for Advanced Study in Mathematics (VIASM), Hanoi

Speaker: Prof. Daniel Tataru, Department of Mathematics, University of California,  USA

Link zoom:

Meeting Id: 8948173518

Passcode: 2023

Title: The small data global well-posedness conjecture for 1D defocusing dispersive flows

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 present some very recent results in this direction. This is joint work with Mihaela Ifrim.

Short Bio: Daniel Tataru grew up in Piatra Neamţ, Romania.  He had an early interest in mathematics, winning the first prize thrice in the National Mathematics Olympiad in Romania, and twice in the International Mathematics Olympiad.  His undergraduate work was devoted to Hamilton-Jacobi equations in Banach spaces in connection to nonlinear semigroups, with Viorel Barbu as advisor;  for this he was awarded the "Gh. Ţiţeica Prize" from the Romanian Academy of Sciences. His graduate and follow up work is on Carleman estimates and their relation to unique continuation and control theory, with Irena Lasiecka and Roberto Triggiani as advisors. Daniel's current interests are centered around the broad area of  nonlinear dispersive equations, with connections to harmonic analysis, geometry, theoretical physics and fluid dynamics.  He is the 2001 recipient of the Bôcher Prize from the American Mathematical Society, a honorary member of the Simion Stoilow Institute of Mathematics in Bucharest, a 2015 recipient of a Humboldt Research Award, and a Simons Investigator since 2013. Since 2014 he is a fellow of the American Academy for Arts and Sciences, and, since 2019, a fellow of the European Academy of Sciences.