Generalized Donaldson-Thomas Invariants via Kirwan Blowups 
-- Michail Savvas, February 2, 2018

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Donaldson-Thomas (abbreviated as DT) theory is a sheaf theoretic
technique of enumerating curves on a Calabi-Yau threefold. Classical
DT invariants give a virtual count of Gieseker stable sheaves
provided that no strictly semistable sheaves exist. This assumption
was later lifted by the work of Joyce and Song who defined
generalized DT invariants using Hall algebras and the Behrend
function, their method being motivic in nature.

In this talk, we will present another approach towards generalized DT
theory, obtaining an invariant as the degree of a virtual cycle
inside a Deligne-Mumford stack. The main components are an adaptation
of Kirwan's partial desingularization procedure and recent results
on the structure of moduli of sheaves on Calabi-Yau threefolds. Based
on joint work with Young-Hoon Kiem and Jun Li.