BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Emanuel Milman (Technion) DTSTART:20200622T111000Z DTEND:20200622T123000Z DTSTAMP:20260423T004755Z UID:GDS/9 DESCRIPTION:Title: Func tional Inequalities on sub-Riemannian manifolds via QCD\nby Emanuel Mi lman (Technion) as part of Geometry and Dynamics seminar\n\n\nAbstract\nWe are interested in obtaining Poincare and log-Sobolev inequalities \non do mains in sub-Riemannian manifolds (equipped with their natural \nsub-Riema nnian metric and volume measure).\n\nIt is well-known that strictly sub-Ri emannian manifolds do not satisfy \nany type of Curvature-Dimension condit ion CD(K\,N)\, introduced by \nLott-Sturm-Villani some 15 years ago\, so w e must follow a different \npath. We show that while ideal (strictly) sub- Riemannian manifolds do \nnot satisfy any type of CD condition\, they do s atisfy a quasi-convex \nrelaxation thereof\, which we name QCD(Q\,K\,N). A s a consequence\, these \nspaces satisfy numerous functional inequalities with exactly the same \nquantitative dependence (up to a factor of Q) as t heir CD counterparts. \nWe achieve this by extending the localization para digm to completely \ngeneral interpolation inequalities\, and a one-dimens ional comparison \nof QCD densities with their "CD upper envelope". We th us obtain the \nbest known quantitative estimates for (say) the L^p-Poinca re and \nlog-Sobolev inequalities on domains in the ideal sub-Riemannian s etting\, \nwhich in particular are independent of the topological dimensio n. For \ninstance\, the classical Li-Yau / Zhong-Yang spectral-gap estimat e holds \non all Heisenberg groups of arbitrary dimension up to a factor o f 4.\n\nNo prior knowledge will be assumed\, and we will (hopefully) expla in \nall of the above notions during the talk.\n LOCATION:https://researchseminars.org/talk/GDS/9/ END:VEVENT END:VCALENDAR