Universal index formula for the moduli of G-bundles
on a Riemann surface -- Constantin Teleman, October 31, 2003

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In this talk, we give a formula for the index of an arbitrary
K-class over the moduli of holomorphic G-bundles on a Riemann
surface. This extends both Verlinde's formula and Witten's
integration formulae. The new formulae are conceptually grounded
in twisted K-theory, but the proof (joint with C. Woodward) is
surprisingly simple, relying only on the symmetries enforced
by Hecke correspondences.