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Stationary Descendents and the Discriminant Modular Form

December 14 at 14:3015:30 CET

TGiF-Seminar: Tropical geometry in Frankfurt (First meeting Winter Semester 2023/24)

Adam Afandi (Universität Münster)

Abstract: By using the Gromov-Witten/Hurwitz correspondence, Okounkov and Pandharipande showed that certain generating functions of stationary descendent Gromov-Witten invariants of a smooth elliptic curve are quasimodular forms. In this talk, I will discuss the various ways one can express the discriminant modular form in terms of these generating functions. The motivation behind this calculation is to provide a new perspective on tackling a longstanding conjecture of Lehmer from the middle of the 20th century; Lehmer posited that the Ramanujan tau function (i.e. the Fourier coefficients of the discriminant modular form) never vanishes. The connection with Gromov-Witten invariants allows one to translate Lehmer’s conjecture into a combinatorial problem involving characters of the symmetric group and shifted symmetric functions.


December 14
14:30 – 15:30 CET


Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß


Martin Ulirsch
Andreas Gross