Algebraic and Arithmetic Geometry Seminar

# Vafa-Witten formulas and generalizations

## by Lothar Göttsche (ICTP, Trieste)

Europe/Rome
Aula Magna (Dipartimento di Matematica)

### Aula Magna

#### Dipartimento di Matematica

Description

25 years ago Vafa and Witten predicted generating functions for the Euler numbers of the moduli spaces of sheaves on algebraic surfaces. In this talk, I review joint work with Martijn Kool to interpret and check these predictions in terms of virtual Euler numbers, and to extend them to finer invariants like $chi_y$ genus. Time permitting I will also mention recent results on Chern numbers of tautological sheaves, and Verlinde type formulas.