BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Vedran Sohinger (University of Warwick) DTSTART:20200505T200000Z DTEND:20200505T210000Z DTSTAMP:20260423T004800Z UID:mitpde/3 DESCRIPTION:Title: G ibbs measures of nonlinear Schrödinger equations as limits of many-body q uantum states\nby Vedran Sohinger (University of Warwick) as part of M IT PDE/analysis seminar spring 2020\n\nLecture held in 2-135.\n\nAbstract\ nGibbs measures of nonlinear Schr¨odinger equations are a fundamental obj ect used to\\nstudy low-regularity solutions with random initial data. In the dispersive PDE community\,\\nthis point of view was pioneered by Bourg ain in the 1990s. We study the problem of the\\nderivation of Gibbs measur es as mean-field limits of Gibbs states in many-body quantum\\nmechanics.\ \nWe present two approaches to this problem. The first one is based on a p erturbative\\nexpansion in the interaction. This expansion is then analyse d by means of Borel resummation techniques and a graphical representation. The second approach is based on a\\nfunctional integral representation. T he latter can be interpreted as a rigorous version of\\nan infinite-dimens ional stationary phase argument. This is joint work with J¨urg Fr¨ohlich \,\\nAntti Knowles\, and Benjamin Schlein.\n LOCATION:https://researchseminars.org/talk/mitpde/3/ END:VEVENT END:VCALENDAR