DAG reading group (Fall 2011)

This is a reading group for students interested in derived algebraic geometry and higher category theory. Our goal is to understand the ideas in Jacob Lurie's work on derived moduli problems, covered in DAG X (and covered in less detail in his ICM address). We will start with the foundations of higher category theory (via quasi-categories).

- The organizational meeting took place on September 6 at 4:30pm in Room 530 in the Science Center.
- The opening lecture (Jacob Lurie) was on Tuesday, September 13 at 4:30
pm in
~~Room 530~~Hall E in the Science Center. - The second talk (Akhil Mathew) on the basics of quasi-categories was on Tuesday, September 20 at 4:30 pm in Hall E in the Science center. Here are notes.
- The third talk (Gijs Heuts) on fibrations of simplicial sets and the Grothendieck construction was on Thursday, September 29th from 5-6:30 pm in Room 530 (note the change).
- The fourth talk (Omar Antolin-Camarena) on stable infinity-categories, following DAG I, will be on Thursday, October 6, from 5-6:30 pm in room 530.
- The fifth talk (Omar Antolin-Camarena) on stable infinity-categories (continuing the fourth), following DAG I, will be on Thursday, October 13, from 5-6:30 pm in room 530.
- The sixth talk (Emily Riehl), on simplicial categories, will be on Thursday, October 20, from 5-6:30 pm in room 530.
- The seventh talk (Akhil Mathew), on rational homotopy theory (following Quillen's paper), will be on Thursday, October 27, from 5-6:30 pm in room 530.
- The eighth meeting will be an informal discussion of Lurie's ICM address (there will not be a talk) on Thursday, Nov. 3.
- The ninth meeting (Alex Perry) will be a survey of deformation theory, on Thursday, Nov. 10.
- The tenth meeting (Alex Perry), on deformation theory, covering an extension of Schlessinger's paper to groupoid-valued functors, will be on Thursday, Nov. 17.
- The eleventh meeting (Omar Antolin-Camerana), on Koszul duality, will be on Thursday, Dec. 1. References are Priddy, "Koszul resolutions," Ginzburg-Kapranov, "Koszul duality for operads," and Getzler-Jones, "Operads, homotopy algebra, and iterated integrals for double loop spaces."

Resources

- Homotopical Algebra by Daniel Quillen
- Model Categories by Mark Hovey
- Simplicial Homotopy Theory by Paul Goerss and Rick Jardine
- Interactions between Homotopy and Algebra summer school notes
- Homology of commutative rings by Daniel Quillen
- Simplicial presheaves by J. F. Jardine

- An untitled book project about symmetric spectra by Stefan Schwede
- Symmetric Spectra by Mark Hovey, Brooke Shipley, and Jeff Smith
- Orthogonal spectra and S-modules by M. A. Mandell and J. P. May
- Model categories of diagram spectra by M. A. Mandell, J. P. May, S. Schwede, and B. Shipley
- DAG I by Jacob Lurie (now in Higher Algebra)

- Simplicial localizations of categories by W. G. Dwyer and Dan Kan
- Model categories and their localizations, by P. Hirschhorn

- Lectures on DG-categories by Bertrand Toen

- A short course on $\infty$-categories by M. Groth
- Higher Topos Theory by Jacob Lurie
- Higher Algebra by Jacob Lurie
- The theory of quasi-categories and its applications by Andre Joyal
- Notes on quasi-categories by Andre Joyal
- Homotopical algebraic geometry I by Bertrand Toen and Gabriele Vezzosi
- A model structure for quasi-categories by Emily Riehl
- A model category structure on the category of simplicial categories by Julia Bergner (see the appendix of HTT for an extension to categories enriched over a monoidal model category)
- Rigidification of quasi-categories by Daniel Dugger and David Spivak

- Jacob Lurie's thesis
- Homotopical algebraic geometry II by Bertrand Toen and Gabriele Vezzosi
- Higher and derived stacks: a global overview by Bertrand Toen
- S^1-Equivariant simplicial algebras and de Rham theory by Bertrand Toen and Gabriele Vezzosi
- Moduli problems for ring spectra by Jacob Lurie
- Thom-Sebastiani and duality for matrix factorizations by Anatoly Preygel

- Champs Algebriques, by Gerard Laumon and Laurent Moret-Bailly
- The Stacks project
- The nLab
- EGA and SGA
- 2009 Gaitsgory seminar
- 2010 DAG seminar at Jerusalem