In recent years great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed to include a variety of techniques from Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of problems connected with dispersive and wave equations, such as the derivation of a certain nonlinear Schrodinger equations from a quantum many-particles system, periodic Strichartz estimates, the concept of energy transfer, the invariance of a Gibbs measure associated to an infinite dimension Hamiltonian system and non-squeezing theorems for such systems when they also enjoy a symplectic structure.
Gigliola Staffilani is Abby Rockefeller Mauze Professor in the Department of Mathematics at MIT. Gigliola was born in Martinsicuro (TE), Italy. After earning an undergraduate degree in Bologna in 1991, she received MS and PhD degrees from the University of Chicago in 1991 and 1995. Following a Szegö Assistant Professorship at Stanford, she had faculty appointments at Stanford, Princeton, and Brown universities before joining the MIT mathematics faculty in 2002 where she became in 2006 the second female full professor of Mathematics.
Amongst her several recognitions, Staffilani was a Sloan Fellow from 2000 to 2002, was a member of the Radcliffe Institute for Advanced Study in 2009-2010, she was elected member of the Massachusetts Academy of Science and a Fellow of the AMS in 2013, and was elected Fellow of the American Academy of Arts and Sciences in 2014. In 2017 she received a Guggenheim Fellowship and a Simons Fellowship in Mathematics. As a member of the department’s edX group, Staffilani received in 2017 also the inaugural MITx Prize for Teaching and Learning in MOOCs by the MIT office of Digital Learning. In 2018 Gigliola has been selected as EMS lecturer.
Gigliola Staffilani works in the broad areas of partial differential equations and Harmonic Analysis, with a particular interest in studying certain PDEs that model nonlinear wave phenomena, including Korteweg-de Vries equation and Schrödinger equation. Gigliola is a frequent collaborator of James Colliander, Markus Keel, Hideo Takaoka and Terence Tao, forming a group known as the “I-team”, whose work was featured in the 2006 Fields Medal citations of group member Tao. Gigliola has published over fifty papers in the area of PDEs and has had six graduate students. She is also an active member of the Association for Women in Mathematics.
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