Office: Science Center 514
Some papers of mine (some original, others expository). Most of these papers were based on work supported by the National Science Foundation under Grant No. 0906194.
| Ambidexterity in K(n)-Local Stable Homotopy Theory.
Joint with Mike Hopkins. Investigates some surprising duality phenomena in the world of K(n)-local homotopy theory. Mostly finished, though it is a bit rough in places. Last update: December 2013.
| 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.
| 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.)
| 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.
| Rational and p-adic Homotopy Theory.
Last update: December 15, 2011.
| Proper Morphisms, Completions, and the Grothendieck Existence
An exposition of some foundational material (described in the title) in the setting of spectral algebraic geometry. Last update: November 8, 2011.
| 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.
| 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.
| 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.
| 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.
| 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).
| 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.
| 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.
| 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.
| Moduli Problems for Ring Spectra.
An informal account of the role of E_n algebras in deformation theory.
| (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.
| Tannaka Duality for Geometric Stacks.
| On Simply-Laced Lie Algebras and their Minuscule Representations.
My undergraduate thesis.
| Some notes that I once prepared on the theory of Hadamard spaces
(metric spaces of nonpositive curvature).
| An exposition of the Borel-Weil-Bott theorem on the cohomology of
holomorphic line bundles over flag varieties.