Chris Woodward

The index formula on the moduli of G-bundles

I will talk about joint work with with Constantin Teleman posted at math.AG/0312154. After discussion some background on abelian and "non-abelian" localization I will describe a short proof of the formulae, conjectured by my co-author, for the index of K-classes over the moduli of holomorphic G-bundles on a Riemann surface. The formulae generalise E. Verlinde's for line bundles, and have Witten's integrals over the moduli space of stable bundles as their large level limits.