QM Research Seminar: The generalized vanishing theorem for the derived blow-ups of quasi-smooth stacks

Speaker: Yu Zhao (IPMU)



Abstract:

In this talk we will briefly introduce a new strategy of introducing birtational geometry to the study of derived algebraic stacks. We will generalize a classical vanishing theorem to holomorphic Kuranishi spaces, i.e. quasi-smooth algebraic stacks. We will explain how this theorem recovers several classical results, including the virtual localization theorem, the semi-orthogonal decomposition of derived category of coherent sheaves and categorification of quantum loop groups.