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

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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.