Summer School 2021: Enumerative Geometry, Physics and Representation Theory

Collection Summer School 2021: Enumerative Geometry, Physics and Representation Theory

Organizer(s) Organising Committee: Andrei Negut, Francesco Sala and Olivier Schiffmann; Scientific Committee: Mina Aganagic, Hiraku Nakajima, Nikita Nekrasov, and Andrei Okounkov
Date(s) 7/5/21 - 7/16/21
linked URL https://indico.math.cnrs.fr/event/5382/
00:00:00 / 00:00:00
31 39

SU(r) Vafa-Witten Invariants and Continued Fractions

By Lothar Gottsche

This is joint work with Martijn Kool and Thies Laarakker. We conjecture a formula for the structure of SU(r) Vafa-Witten invariants of surfaces with a canonical curve, generalizing a similar formula proven by Laarakker for the monopole contribution. This expresses the Vafa-Witten invariants in terms of some universal power series and Seiberg-Witten invariants. Using computations on nested Hilbert schemes we conjecturally determine these universal power series for r at most 5 in terms of theta functions for the A_{r-1} lattice and Ramanujan's continued fractions.

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