BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Vladimir Matveev (Universität Jena) DTSTART:20210223T160000Z DTEND:20210223T170000Z DTSTAMP:20260423T052953Z UID:DGSTO/10 DESCRIPTION:Title: N ijenhuis geometry\, multihamiltonian systems of hydrodynamic type and geod esic equivalence\nby Vladimir Matveev (Universität Jena) as part of D ifferential Geometry Seminar Torino\n\n\nAbstract\nWe connect two a priori unrelated topics\, theory of geodesically equivalent metrics in different ial geometry\, and theory of compatible infinite dimensional Poisson brack ets of hydrodynamic type in mathematical physics. \n\nNamely\, we prove t hat a pair of geodesically equivalent metrics such that one is flat produc es a pair of such brackets. We construct Casimirs for these brackets and t he corresponding commuting flows. \n\nThere are two ways to produce a larg e family of compatible Poisson structures from a pair of geodesically equi valent metrics one of which is flat. One of these families is $(n+1)(n+2) /2$ dimensional\; we describe it completely and show that it is maximal. A nother has dimension $\\le n+2$ and is\, in a certain sense\, polynomial. We show that a nontrivial polynomial family of compatible Poisson structur es of dimension $n+2$ is unique and comes from a pair of geodesically equi valent metrics.\n\nThe talk based on a series of joint publications with A . Bolsinov (Lboro) and A. Konyaev (Moscow)\; the most related one is https ://arxiv.org/abs/2009.07802\n LOCATION:https://researchseminars.org/talk/DGSTO/10/ END:VEVENT END:VCALENDAR