Recent Progress On The Donaldson-Thomas Theory eBook

Recently, a deeper structure of the moduli spaces of coherent sheaves on Calabi-Yau 3-folds was found through derived algebraic geometry. These moduli spaces admit shifted symplectic structures and the associated d-critical structures, which lead to refined versions of DT invariants such as cohomological DT invariants. The idea of cohomological DT invariants led to a mathematical definition of the Gopakumar-Vafa invariant, which was firstproposed by Gopakumar-Vafa in 1998, but its precise mathematical definition has not been available until recently.

This book surveys the recent progress on DT invariants and related topics, with a focus on applications to curve-counting theories.