BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andrea Nahmod (University of Massachusetts Amherst -- USA) DTSTART:20220505T153000Z DTEND:20220505T163000Z DTSTAMP:20260423T040039Z UID:SIAM-PDE/20 DESCRIPTION:Title: Gibbs measures and propagation of randomness under the flow of nonlinear dispersive PDE\nby Andrea Nahmod (University of Massachusetts Amherst -- USA) as part of Seminar In the Analysis and Methods of PDE (SIAM PDE)\ n\n\nAbstract\nIn groundbreaking work\, Bourgain ’96 put forward a rando m data theory to study the existence of strong solutions on the statistica l ensemble of Gibbs measures associated to dispersive equations. Despite n umerous follow-up works to those of Bourgain’s\, fundamental questions r emained open. How does a given initial random data get transported by a no nlinear flow ? If it is Gaussian initially\, how does this Gaussianity pr opagate? What is the description of the solution beyond the linear evoluti on?\n\nIn recent work\, joint with Yu Deng and Haitian Yue\, we developed the theory of random tensors\, a powerful new framework which allows us to unravel the propagation of randomness under the NLS flow beyond the linea r evolution of random data\, and answer these questions in an optimal rang e relative to what we define as the probabilistic scaling. In particular\ , we establish the invariance of Gibbs measures for 2D NLS and 3D Hartree NLS equations using the method of random averaging operators\, a first ord er approximation to the full random tensor theory. \n\nIn this talk we wil l describe these results\, and explain the ideas behind them. We conclude with some open problems and within this context present new work\, joint with Bjoern Bringmann\, Yu Deng and Haitian Yue establishing the invarian ce of the 3D Gibbs measure under the flow of the nonlinear wave equation.\ n\nBio Andrea R. Nahmod is Professor of Mathematics at the University of M assachusetts Amherst. Her research lies at the interface of nonlinear Four ier and harmonic analysis\, and the theory of partial differential equatio ns. Some of her recent work aims at gaining a quantitative understanding o f the propagation of randomness under the nonlinear evolution of dispersiv e PDE. Nahmod is a Fellow of the American Mathematical Society\; a recipi ent of the Sargent-Faull Fellowship at Harvard’s Radcliffe Institute for Advanced Study\, and of a Simons Foundation Fellowship. Nahmod was twice a member of the Institute for Advanced Study at Princeton and held Simons ’ Professorships at MSRI\, Berkeley and at CRM Montreal. She delivered a n invited address at the 2021 Joint Mathematical Meetings of the AMS.\n LOCATION:https://researchseminars.org/talk/SIAM-PDE/20/ END:VEVENT END:VCALENDAR