BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Steve Zelditch (Northwestern University) DTSTART:20200602T160000Z DTEND:20200602T170000Z DTSTAMP:20260423T022628Z UID:Geolis/4 DESCRIPTION:Title: P robabilistic aspects of toric Kähler geometry\nby Steve Zelditch (Nor thwestern University) as part of Geometria em Lisboa (IST)\n\n\nAbstract\n Let $(M\, \\omega\, L)$ be a polarized toric Kahler manifold with polytope $P$. Associated to this data is a family $\\mu_k^x$ of probability measur es on $P$ parametrized by $x \\in P.$ They generalize the multi-nomial mea sures on the simplex\, where $M = \\mathbb{CP}^n$ and $\\omega$ is the Fub ini-Study measure. As is well-known\, these measures satisfy a law of larg e numbers\, a central limit theorem\, a large deviations principle and ent ropy asymptotics. The measure of maximal entropy in this family correspond s to the center of mass $x$ of $P$. All of these results generalize to any toric Kahler manifold\, except the center of mass result\, which holds fo r Fano toric Kahler-Einstein manifolds.\n\nJoint work with Peng Zhou and P ierre Flurin.\n LOCATION:https://researchseminars.org/talk/Geolis/4/ END:VEVENT END:VCALENDAR