A Darboux theorem for symplectic derived stacks                          
-- Chris Brav, January 31, 2014

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We discuss the notion of a symplectic form of degree
k on a derived stack and prove a Darboux theorem for symplectic
forms of negative degree. As a corollary, we show that the
stack of coherent sheaves on a Calabi-Yau threefold admits an
atlas consisting of critical loci of functions on smooth
varieties. If time permits, we describe how, under an
additional hypothesis, this provides a categorification of
Donaldson-Thomas invariants. This is joint work with various
subsets of Ben-Bassat, Bussi, Dupont, Joyce, and Szendroi.