Tautological Hecke correspondence and K-theory of the moduli space of parabolic vector bundles

ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR

The Verlinde formula, an expression for the Hilbert function of the moduli spaces of vector bundles on Riemann surfaces, is one of the most beautiful results in enumerative geometry. In this talk, I will describe a generalisation of this result in the case of the moduli space of rank-2 parabolic bundles: a calculation of Euler characteristics of universal vector bundles. The result is motivated by the formula of Teleman and Woodward for the index of K-theory classes over the moduli stack of bundles on Riemann surfaces. The approach uses a wall-crossing technique and the tautological Hecke correspondence.