BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Danilo Lewański (IHES and IPhT) DTSTART:20211119T080000Z DTEND:20211119T090000Z DTSTAMP:20260423T024531Z UID:CGP-MP/18 DESCRIPTION:Title: Cohomological field theories and BKP integrability: Omega classes times Wi tten-classes\nby Danilo Lewański (IHES and IPhT) as part of IBS-CGP M athematical Physics Seminar\n\n\nAbstract\nThere is a deep interaction bet ween Cohomological field theories (CohFTs)\, introduced by Kontsevich and Manin\, and integrable hierarchies. For instance\, the celebrated Witten-K ontsevich result shows that the trivial CohFT gives rise to a solution of the KdV integrable hierarchy. As another example\, Kazarian’s theorem sh ows that the Hodge CohFT gives rise to a solution of the KP hierarchy\, an d so do Hurwitz numbers\, which by ELSV formula are descendant integrals o f the Hodge CohFT. The change of variable which carries the partition func tion of Hurwitz numbers into the partition function of pure descendant Hod ge integrals is triangular and KP-preserving\, it is in fact essentially g iven by the Topological Recursion spectral curve in the sense of Eynard an d Orantin. \n\nWe study spin-Hurwitz numbers (not to be confused with comp leted cycles Hurwitz numbers) enumerating branches Riemann covers weighted by the parity of theta characteristics. They obey the BKP integrable hier archy. We prove that the Topological Recursion conjecture for these number s is equivalent to their underlying CohFT to be an explicit product betwee n Witten’s class and Omega-classes computed by Chiodo. The Topological R ecursion conjecture has recently been proved by Alexandrov and Shadrin in a more general framework for BKP integrability.\n LOCATION:https://researchseminars.org/talk/CGP-MP/18/ END:VEVENT END:VCALENDAR