MS Seminar (Mathematics - String Theory)

Speaker: Gabriele Vezzosi (U of Firenze)
Title: Introduction to derived algebraic geometry
Date: Tue, Mar 20, 2018, 10:30 - 12:00
Place: Seminar Room B
Abstract: We will give an informal introduction to derived algebraic geometry and to symplectic and Poisson geometry inside derived algebraic geometry, and concentrate on examples that will be useful in the remaining two talks. Then we will explain the problem of defining a pointed formal neighbourhood in algebraic geometry, give one solution, explain how to get from this formal gluing results of (pseudo-)perfect complexes and G-bundles, given a closed substack (or a flag of these) in a fixed stack, and speculate about possible relations with the Geometric Langlands Program for surfaces.

In the final lecture we will consider moduli spaces of (possibly irregular) connections on higher dimensional varieties, study their derived Poisson structures and construct their symplectic leaves by means of a derived analog of quasi-hamiltonian reduction construction.
Remarks: Prof. Toen and Prof Vessozi's talk (on March 20) are combined: