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SUMMARY:Adam Afandi (Universität Münster)
DTSTART:20231214T133000Z
DTEND:20231214T143000Z
DTSTAMP:20260422T172521Z
UID:TGiZ/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TGiZ/56/">St
 ationary Descendents and the Discriminant Modular Form</a>\nby Adam Afandi
  (Universität Münster) as part of Tropical Geometry in Frankfurt/Zoom TG
 iF/Z\n\n\nAbstract\nBy using the Gromov-Witten/Hurwitz correspondence\, Ok
 ounkov and Pandharipande showed that certain generating functions of stati
 onary descendent Gromov-Witten invariants of a smooth elliptic curve are q
 uasimodular forms. In this talk\, I will discuss the various ways one can 
 express the discriminant modular form in terms of these generating functio
 ns. The motivation behind this calculation is to provide a new perspective
  on tackling a longstanding conjecture of Lehmer from the middle of the 20
 th century\; Lehmer posited that the Ramanujan tau function (i.e. the Four
 ier coefficients of the discriminant modular form) never vanishes. The con
 nection with Gromov-Witten invariants allows one to translate Lehmer's con
 jecture into a combinatorial problem involving characters of the symmetric
  group and shifted symmetric functions.\n
LOCATION:https://researchseminars.org/talk/TGiZ/56/
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