Higher rank Donaldson-Thomas invariants of K3 surfaces -- Benjamin Bakker, September 24, 2010

Virtual curve counts have been defined for threefolds by integration against virtual classes on moduli spaces of stable maps (Gromov-Witten theory), ideal sheaves (Donaldson-Thomas theory), and stable pairs (Pandharipande-Thomas theory); all three theories are conjecturally equivalent. The Gromov-Witten theory of K3 surfaces has recently been calculated and shown to be governed by classical modular forms by Maulik, Pandharipande, and Thomas. In joint work with Andrei Jorza, we define and fully compute an analog of Donaldson-Thomas theory on K3 surfaces via stable pairs and investigate the modularity properties.