Derived algebraic geometry

Derived Algebraic Geometry (seminar)

Lennart and I are organising a Derived Algebraic Geometry seminar in Utrecht starting May 9th, 2019. We should cover some of the basics of derived algebraic geometry (through the eyes of Toën and Lurie) and eventually cover some topics like the construction of virtual fundamental classes and shifted symplectic structures. We are on a hiatus now, until we can find some mutual time and topics.

Here is the current timetable. All seminars will take place in room 610 in the Hans Freudenthalgebouw. If you would like to volunteer to give a seminar then either contact Lennart or myself.

Thursday May 9 (09:30)

Foundations and motivations (Lennart Meier)

Thursday May 23 (10:30)

Derived schemes (Jack Davies)

Thursday June 6 (10:30)

Virtual fundamental classes (Ties Laarakker)

Thursday June 27 (10:30)

Fibre products and quasi-coherent sheaves in DAG (Sergej Monavari)

Thursday November 14 (10:00)

Derived moduli problems and stacks (Jack Davies)

Thursday November 28 (10:00)

Cotangent complex in DAG (Tommy Lundemo)

Thursday December 12 (10:00)

Derived deformation theory (Martijn Kool and Gijs Heuts)

Below is the current draft of the notes (updated 16.12.2019).

Here are also some links to some papers we may discuss.

• Derived Algebraic Geometry by Toën

• Simplicial Methods for Operads and Algebraic Geometry by Moerdijk and Toën

• Moduli of objects in dg-categories by Toën and Vaquié

• Shifted Symplectic Structures by Pantev, Toen, Vaquie, and Vezzosi