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

<p>

A natural class of vector bundles arises on the
moduli space of curves by considering relative moduli spaces of
sheaves over M<sub>g</sub> 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.