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SUMMARY:Paul Norbury (University of Melbourne)
DTSTART:20210423T010000Z
DTEND:20210423T020000Z
DTSTAMP:20260423T024519Z
UID:CGP-MP/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CGP-MP/7/">E
 numerative geometry via the moduli space of super Riemann surfaces</a>\nby
  Paul Norbury (University of Melbourne) as part of IBS-CGP Mathematical Ph
 ysics Seminar\n\n\nAbstract\nMumford initiated the calculation of many alg
 ebraic topological invariants over the moduli space of Riemann surfaces in
  the 1980s\, and Witten related these invariants to two dimensional gravit
 y in the 1990s. This viewpoint led Wittento a conjecture\, proven by Konts
 evich\, that a generating function for intersection numbers on the moduli 
 space of curves is a tau function of the KdV hierarchy\, now known as the 
 Kontsevich-Witten tau function\, which allowed their evaluation. In 2004\,
  Mirzakhaniproduced another proof of Witten's conjecture via the study of 
 Weil-Petersson volumes of the moduli space using hyperbolic geometry. In t
 his lecture I will describe a new collection of integrals over the moduli 
 space of Riemann surfaces whose generating functionis a tau function of th
 e KdV hierarchy\, known as the Brezin-Gross-Witten tau function. I will sk
 etch a proof of this result that uses an analogue of Mirzakhani's argument
  applied to the moduli space of super Riemann surfaces - defined by replac
 ing the fieldof complex numbers with a Grassman algebra - which uses recen
 t work of Stanford and Witten. This appearance of the moduli space of supe
 r Riemann surfaces to solve a problem over the classical moduli space is d
 eep and surprising.\n
LOCATION:https://researchseminars.org/talk/CGP-MP/7/
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