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
Stable Infinity Categories. The first bit of my (revised) PhD thesis. Last update: March 31, 2008.	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: March 31, 2008.	DAGII
Commutative Algebra. The third bit of my PhD thesis. It is an introduction to the theory of commutative ring spectra from the higher-categorical point of view. Last update: March 31, 2008.	DAGIII
Deformation Theory. The fourth bit of my PhD thesis. It discusses the deformation theory of E-infinity ring spectra. Last update: March 31, 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: March 31, 2008.	DAGV
Higher Topos Theory. A draft of my book on higher category theory. Last update: March 31, 2008. Proofs of some basic facts have been reworked to avoid topological arguments. Comments welcome! (Especially regarding typos, mathematical errors, or points where the exposition is unclear.) (Warning: contents may have shifted so that references from the other papers are misnumbered; this will be corrected soon.)	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