BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hovhannes Khudaverdian DTSTART:20210331T162000Z DTEND:20210331T180000Z DTSTAMP:20260423T010139Z UID:GDEq/33 DESCRIPTION:Title: Od d symplectic geometry in the BV-formalism\nby Hovhannes Khudaverdian a s part of Geometry of differential equations seminar\n\nLecture held in ro om 304 of the Independent University of Moscow.\n\nAbstract\nOdd symplecti c geometry was considered by physicists as an exotic counterpart of even s ymplectic geometry. Batalin and Vilkovisky changed this\npoint of view by the seminal work considering the quantisation of general theory in Lagrang ian framework\, where they considered odd symplectic superspace of fields and antifields. [In the case of Lie group of symmetries BV receipt is redu ced to the standard Faddeev-Popov method.]\n\nThe main ingredient of the t heory\, the exponent of the master action\, is defined by the function $f$ such that $\\Delta f=0$\, where $\\Delta$ is second order differential op erator of the second order: $\\Delta=\\frac{\\partial^2}{\\partial x^i \\p artial\\theta_i}$\, ($x^i\,\\theta_j$ are the Darboux coordinates of an od d symplectic superspace.) This operator has no analogy in the standard sym plectic geometry.\n\nI consider in this talk the main properties of the BV -formalism geometry.\n\nThe $\\Delta$-operator is defined in geometrical c lear way\, and this operator depends on the volume form.\n\nIt is suggeste d the canonical operator $\\Delta$ on half-densities. This operator is the proper framework for BV geometry. We also study the groupoid property of BV master-equation\; this leads us to the notion of BV groupoid. We also d iscuss some constructions of invariants for odd symplectic structure.\n LOCATION:https://researchseminars.org/talk/GDEq/33/ END:VEVENT END:VCALENDAR