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We meet Tuesdays 3:15-5:15 pm UTC via Zoom. We also have a Discord discussion channel.

Timetable #

Date Topic Speaker Notes References
19.10 Introduction to derived algebraic geometry Zachary Gardner PDF [CS19, Appendix to Lecture II], [CS21, §5.1.4], [Lur, §1-2], [Lur17a, §1.1.2 & 1.2.1], [May99, Ch. 5], [Toe14, §1-2]
26.10 Categorified algebraic geometry Zachary Gardner PDF [Ras18], [Toe]
09.11 Derived schemes Zachary Gardner PDF [Lur17b, Ch. 6], [Lur18, §1.3], [preschema17, Lecture 1]
16.11 Quasicoherent sheaves Zachary Gardner PDF [Kha16, §0.4-5], [Lur17a, §4.7], [Lur18, §5.6.5], [preschema17, Lecture 1-2]
30.11 The cotangent complex Jeroen Hekking PDF [dac, Lecture 3], [Lur], [Lur18]
07.12 Derived blow-ups Jeroen Hekking PDF [Lur], [Lur18], [Vez10]

Learning Goals #

The following are things we want to make sure we cover (at least in some capacity).

  • Derived intersection theory
  • Derived deformation theory
  • Koszul duality
  • Hoschschild-Konstant-Rosenberg (HKR) theorem

The following are things we would (maybe) like to work towards (though we may not get to them).

  • Virtual fundamental classes
  • Derived algebraic cobordism
  • Gromov-Witten theory
  • Topological modular forms

Philosophy #

Here are some aspects of our philosophy.

  • We want to think in terms of homotopy types and so avoid things like model structures as much as possible.
  • We want to avoid or ignore set-theoretic issues whenever possible.
  • We want to “play around” with the mathematics, focusing mainly on examples and questions rather than formalism.

References #

Derived Algebraic Geometry

Infinity Categories

Homotopy Theory

Categorified Algebraic Geometry and Stacks

Miscellaneous

Contact #

Please get in touch if you want to participate or have comments/suggestions:

Zachary: website, mail

Aaron: website, mail

Other Learning Groups #

There are many other learning groups out there for DAG and related topics. Here are just a few.