Résumé |
The Darboux theorem states that symplectic manifolds are locally cotangent
bundles. An analog in derived algebraic geometry is that shifted symplectic
schemes are locally twisted cotangent bundles. This can be applied to moduli
spaces of sheaves on Calabi-Yau varieties, which is a crucial ingredient in
Donaldson-Thomas theory.
In this talk, I will present a generalization of the derived Darboux theorem to
families and to stacks. As an application of the family version, I will discuss
counting surfaces on CY4, which is joint work with Younghan Bae and Martijn Kool.
As an application of the stacky version, I will explain the construction of
cohomological Hall algebras for CY3, which is joint work with Tasuki Kinjo and
Pavel Safronov. |