Tautological Hecke correspondence and K-theory of the moduli space of parabolic vector bundles
ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR
Date
Thursday, April 7, 2022 13:00 - 15:00
Speaker
Olga Trapeznikova (Université de Genève)
Location
Heinzel Seminar Room (I21.EG.101), Office Building West
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
Tamas Hausel
Contact
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.