BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ekaterina Shemyakova DTSTART:20241127T162000Z DTEND:20241127T180000Z DTSTAMP:20260423T010422Z UID:GDEq/120 DESCRIPTION:Title: O n differential operators generating higher brackets\nby Ekaterina Shem yakova as part of Geometry of differential equations seminar\n\n\nAbstract \nOn supermanifolds\, a Poisson structure can be either even\, correspondi ng to a Poisson bivector\, or odd\, corresponding to an odd Hamiltonian qu adratic in momenta. An odd Poisson bracket can also be defined by an odd s econd-order differential operator that squares to zero\, known as a "BV-ty pe" operator.\n\nA higher analog\, $P_\\infty$ or $S_\\infty$\, is a serie s of brackets of alternating parities or all odd\, respectively\, that sat isfy relations that are higher homotopy analogs of the Jacobi identity. Th ese brackets are generated by arbitrary multivector fields or Hamiltonians . However\, generating an $S_\\infty$-structure by a higher-order differen tial operator is not straightforward\, as this would violate the Leibniz i dentities. Kravchenko and others studied these structures\, and Voronov ad dressed the Leibniz identity issue by introducing formal $\\hbar$-differen tial operators.\n\nIn this talk\, we revisit the construction of an $\\hba r$-differential operator that generates higher Koszul brackets on differen tial forms on a $P_\\infty$-manifold.\n\nIt is well known that a chain map between the de Rham and Poisson complexes on a Poisson manifold at the sa me time maps the Koszul bracket of differential forms to the Schouten brac ket of multivector fields. In the $P_\\infty$-case\, however\, the chain m ap is also known\, but it does not connect the corresponding bracket struc tures. An $L_\\infty$-morphism from the higher Koszul brackets to the Scho uten bracket has been constructed recently\, using Voronov's thick morphis m technique. In this talk\, we will show how to lift this morphism to the level of operators.\n\nThe talk is partly based on joint work with Yagmur Yilmaz.\n LOCATION:https://researchseminars.org/talk/GDEq/120/ END:VEVENT END:VCALENDAR