Bertrand Toën (Université Paul Sabatier, Toulouse)

Simplicial presheaves and derived geometries

The purpose of this course is to give an introduction to the emerging subject of derived algebraic geometry as well as its analytic and differential analogs. The course is intended to cover a large part of the subject, starting from the very first definitions of derived varieties and derived stacks and ending with more recent developments and applications. This approach to derived geometry will be based on model category theory, but all along the course an alternative, equivalent approach based on quasi-category theory (as in Joyal’s lectures) will be presented. Although this course is introductory, some basic knowledge of model categories, sheaf theory, and algebraic geometry is required.