Derived algebraic geometry in mathematical physics

par Prof. Alexander Schenkel (Nottingham)

vendredi 21 avr. 2023, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (Bâtiment Braconnier)

Derived algebraic geometry is a powerful geometric framework which plays an increasingly important role both in the foundations of algebraic geometry and in mathematical physics. It introduces a refined concept of ‘space’, the so-called derived stacks, that is capable to describe correctly geometric situations that are problematic in traditional approaches, such as non-transversal intersections and quotients by non-free group actions. In this talk I will give a very basic introduction to derived algebraic geometry, focussing in particular on its more concrete and computational aspects. I will then illustrate the potential of this framework for new developments in mathematical physics by studying two applications: 1.) The derived critical locus of a function f : [X/G] —> k on a quotient stack, and 2.) the quantization of a derived cotangent stack T*[X/G] over a quotient stack.

 

This talk is based on joint works with Benini and Safronov [arXiv:2104.14886] and Benini and Pridham [arXiv:2201.10225].