Higher Algebra. A new version of my second book. Much of the first chapter has been rewritten, and I have added a new chapter about Goodwillie's calculus of functors. Comments and corrections are always welcome. Last update: August 2012.	pdf
Higher Topos Theory. The latest version of my book on higher category theory. The book has now gone to press, but I will continue to keep an updated copy here (big thanks to Bruce Williams for showing me how to fix the formatting). Last update: February 2012 (Fixed some more errors.)	pdf
Representability Theorems. A proof of Artin's representability theorem for spectral Deligne-Mumford stacks. (Essentially the main result of my thesis, but in a somewhat different setting.) This will be the last of the DAG papers for a while. First Draft: March 14, 2012.	DAGXIV
Rational and p-adic Homotopy Theory. Last update: December 15, 2011.	DAGXIII
Proper Morphisms, Completions, and the Grothendieck Existence Theorem. An exposition of some foundational material (described in the title) in the setting of spectral algebraic geometry. Last update: November 8, 2011.	DAGXII
Descent Theorems. Some descent theorems for quasi-coherent sheaves and quasi-coherent stacks in the setting of spectral algebraic geometry. Last update: September 28, 2011.	DAGXI
Formal Moduli Problems. A study of formal moduli problems in the setting of commutative and noncommutative derived algebraic geometry. Contains detailed proofs of the results claimed in my ICM address. Rough draft. Last update: September 1, 2011.	DAGX
Closed Immersions. A study of closed immersions in spectral algebraic geometry, and the operation of gluing along closed immersions. As an application we develop the rudiments of a theory of derived complex analytic spaces. Last update: June 2011.	DAGIX
Quasi-Coherent Sheaves and Tannaka Duality Theorems. An exposition of the theory of quasi-coherent sheaves in the setting of spectral algebraic geometry. Last update: May 2011.	DAGVIII
Spectral Schemes. Introduces the definition of scheme and Deligne-Mumford stack in the setting of algebraic geometry over structured ring spectra. Last update: June 2011 (updated version has a new section on fpqc descent).	DAGVII
Structured Spaces. The fifth bit of my PhD thesis. It described a general theory of "spaces" (i.e., infty-topoi) with structure sheaves, like sheaves of commutative rings. Last update: February 2011.	DAGV
Survey article on elliptic cohomology. This is a survey of the theory of elliptic cohomology, with emphasis on the the insight offered by derived algebraic geometry. (Updated April 2007). More details will be available later.	pdf
Expository article on topological field theories. This paper gives an informal account of a proof of the Baez-Dolan cobordism hypothesis and related matters. (Last update: May 2009) A more detailed account will appear here eventually.	pdf
Moduli Problems for Ring Spectra. An informal account of the role of E_n algebras in deformation theory.	Paper.
(infty,2)-Categories and the Goodwillie Calculus I. This is mostly devoted to some of the technical details of particular models for the theory of (infty,2)-categories. The ultimate goal is to give some applications to the Goodwillie calculus, but there's very little of that in this paper. Last update: October 2009.	GI
Tannaka Duality for Geometric Stacks. A preprint.	pdf
On Simply-Laced Lie Algebras and their Minuscule Representations. My undergraduate thesis.	pdf
Some notes that I once prepared on the theory of Hadamard spaces (metric spaces of nonpositive curvature).	pdf
An exposition of the Borel-Weil-Bott theorem on the cohomology of holomorphic line bundles over flag varieties.	pdf