Seminars

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ABSTRACT: Counting sheaves on curves, or more precisely, computing intersection pairings on the moduli space of semistable vector bundles on curves, has been a classical problem in enumerative geometry. The computation was first done by Witten using physical methods; his formula was later proved by Jeffrey–Kirwan, and generalized by Jeffrey–Kiem–Kirwan–Woolf to the case when the rank and the degree are not coprime. In this talk, I will introduce a new approach to the problem using the wall-crossing formalism developed by Joyce. This allows us to obtain a new formula for these intersection pairings, different from but equivalent to Witten's. The new formula involves a divergent infinite sum in Joyce's vertex algebra. It would be interesting to explore possible geometric or physical interpretations of this formula.