BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Frol Zapolsky (University of Haifa) DTSTART:20201125T121000Z DTEND:20201125T133000Z DTSTAMP:20260423T004911Z UID:GDS/17 DESCRIPTION:Title: Rel ative symplectic cohomology and ideal-valued measures\nby Frol Zapolsk y (University of Haifa) as part of Geometry and Dynamics seminar\n\n\nAbst ract\nIn a joint work in progress together with A. Dickstein\, Y. Ganor\, and \nL. Polterovich we prove new symplectic rigidity results. First\, we \ncategorify the notion of a heavy subset of a symplectic manifold (due \n to Entov-Polterovich)\, and in particular provide a simple algebraic \ncri terion which guarantees that two heavy sets intersect. Next\, we \ntreat i nvolutive maps defined on a symplectic manifold M\; a smooth \nmap M -> B is involutive if pullbacks of smooth functions on B Poisson \ncommute. For such maps we prove a refinement of Entov-Polterovich's \nnondisplaceable fiber theorem\, as well as a symplectic Tverberg-type \ntheorem\, which ro ughly says that each involutive map into a manifold \nof sufficiently low dimension has a fiber which intersects a wide \nfamily of subsets of M.\n\ nAll of these results are proved using a generalized version of Gromov's \ nnotion of ideal-valued measures\, which furnish an easily digestible \nwa y to package the relevant information. We construct such measures \nusing relative symplectic cohomology\, an invariant recently introduced \nby U. Varolgunes\, who also proved the Mayer-Vietoris property for it\, \non whi ch our work relies in a crucial manner. Our main technical \ninnovation is the relative symplectic cohomology of a pair\, whose \nconstruction is in spired by homotopy theory.\n LOCATION:https://researchseminars.org/talk/GDS/17/ END:VEVENT END:VCALENDAR