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:20260404T131149Z UID:GDS/9 DESCRIPTION:Title: Functional Inequalities on sub-Riemannian manifolds via QCD\nby Ema nuel Milman (Technion) as part of Geometry and Dynamics seminar\n\n\nAbstr act\nWe are interested in obtaining Poincare and log-Sobolev inequalities \non domains in sub-Riemannian manifolds (equipped with their natural \nsu b-Riemannian metric and volume measure).\n\nIt is well-known that strictly sub-Riemannian manifolds do not satisfy \nany type of Curvature-Dimension condition CD(K\,N)\, introduced by \nLott-Sturm-Villani some 15 years ago \, so we must follow a different \npath. We show that while ideal (strictl y) sub-Riemannian manifolds do \nnot satisfy any type of CD condition\, th ey do satisfy a quasi-convex \nrelaxation thereof\, which we name QCD(Q\,K \,N). As a consequence\, these \nspaces satisfy numerous functional inequa lities with exactly the same \nquantitative dependence (up to a factor of Q) as their CD counterparts. \nWe achieve this by extending the localizati on paradigm to completely \ngeneral interpolation inequalities\, and a one -dimensional comparison \nof QCD densities with their "CD upper envelope". We thus obtain the \nbest known quantitative estimates for (say) the L^p -Poincare and \nlog-Sobolev inequalities on domains in the ideal sub-Riema nnian setting\, \nwhich in particular are independent of the topological d imension. For \ninstance\, the classical Li-Yau / Zhong-Yang spectral-gap estimate holds \non all Heisenberg groups of arbitrary dimension up to a f actor of 4.\n\nNo prior knowledge will be assumed\, and we will (hopefully ) explain \nall of the above notions during the talk.\n LOCATION:https://stable.researchseminars.org/talk/GDS/9/ END:VEVENT END:VCALENDAR