Abstract:
We will speak about Donaldson-Thomas theory as a motivating example to introduce the theory of derived symplectic structures by Pantev, Toen, Vaquie and Vezzosi and the theory of derived critical loci by Joyce. We will then use these theories to prove a Darboux theorem for symplectic derived schemes and to construct on them perverse sheaves which are central in the problem of categorification.
This is a joint work with Ben-Bassat, Brav, Dupont, Joyce, Meinhardt and Szendroi.