The Chern classes of the Verlinde bundles -- Alina Marian, February 28, 2014

A natural class of vector bundles arises on the moduli space of curves by considering relative moduli spaces of sheaves over Mg and associated theta divisors. Their ranks are given by the well-studied Verlinde numbers. I will first discuss a formula for the first Chern class of the Verlinde bundles, obtained jointly with Dragos Oprea and Rahul Pandharipande. I will then explain how Teleman's work on semisimple cohomological field theories can be used to derive the Chern characters of the extensions of the Verlinde bundles to the moduli space of stable curves. This latter part is based on joint work with D. Oprea, R. Pandharipande, A. Pixton and D. Zvonkine.