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
Stable Infinity Categories. The first bit of my (revised) PhD thesis. Last update: May 2009.	DAGI
Noncommutative Algebra. The second bit of my PhD thesis. It contains material on monoidal infinity categories, a version of the Barr-Beck theorem, and an introduction to the theory of associative ring spectra. Last update: May 2009.	DAGII
Commutative Algebra. The third bit of my PhD thesis. This has been substantially rewritten, and now contains an exposition of a higher-categorical theory of colored operads; the end includes some applications to the study of commutative ring spectra. Last update: May 2009.	DAGIII
Deformation Theory. The fourth bit of my PhD thesis. It discusses the deformation theory of E-infinity ring spectra. Last update: May, 2008.	DAGIV
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: May 2009.	DAGV
(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: May 2009.	GI
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 (apologies for the inconvenient formatting). Last update: May 2009.	pdf
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