**The International Center for Mathematical Sciences – Sofia (ICMS-Sofia)**

**presents**

## ICMS Geometry Seminar

24.01.2024, 16:00, Sofia time

ICMS-Sofia, Room 403 and via Zoom

# Introduction to Derived Algebraic Geometry and deformation theory

## Yingdi Qin, IMI-BAS

This will be an introductory talk on derived algebraic geometry with emphasis on the application to deformation theory. Deformation theory studies the formal neighborhoods of moduli spaces(in particular, the 1-st order deformations and obstructions to extension). The cotangent bundle of the moduli is the 1-st order approximation of the formal neighborhood. Since the moduli space is in general singular and stacky, we have to replace the cotangent bundle by cotangent complex. And derived algebraic geometry provides the suitable framework to study cotangent complex. I will also mention Lurie’s theorem on formal moduli problem. As an application, the cotangent complex of a moduli space together with its shifted Lie algebra structure completely determines the formal neighborhood of the moduli space.