BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:David Ben-Zvi (UT Austin) DTSTART:20210322T190000Z DTEND:20210322T200000Z DTSTAMP:20260423T035914Z UID:WHCGP/29 DESCRIPTION:Title: E lectric-Magnetic Duality between Periods and L-functions\nby David Ben -Zvi (UT Austin) as part of Western Hemisphere colloquium on geometry and physics\n\n\nAbstract\nI will describe joint work with Yiannis Sakellaridi s and Akshay Venkatesh\, in\nwhich ideas originating in quantum field theo ry are applied to a problem in\nnumber theory.\n\nA fundamental tool in nu mber theory\, the relative Langlands program\, is\ncentered on the represe ntation of L-functions of Galois representations as\nintegrals of automorp hic forms. However\, the data that naturally index these\nperiod integrals (spherical varieties for a reductive group G) and the\nL-functions (repre sentations of the Langlands dual group G^) don't seem to line\nup\, making the search for integral representations somewhat of an art. \n\nWe presen t an approach to this problem via the Kapustin-Witten interpretation\nof t he [geometric] Langlands correspondence as electric-magnetic duality for\n 4-dimensional supersymmetric gauge theory. Namely\, we rewrite the relativ e \nLanglands program as duality in the presence of boundary conditions. A s a\nresult the partial correspondence between periods and L-functions is embedded\nin a natural duality between Hamiltonian actions of the dual gro ups.\n LOCATION:https://researchseminars.org/talk/WHCGP/29/ END:VEVENT END:VCALENDAR