Jacob Lurie's Home Page Jacob Lurie's Home Page

Office: Science Center 514
Office Hours: Wednesday 2-3 (or by appointment).
email: lurie
Department of Mathematics, Harvard University, Cambridge.

  • Course website for Math 281 (Algebraic K-theory and Manifold Topology; offered Fall 2014): here.
  • Course website or Math 282y (offered Spring 2014): here.
  • Course website or Math 114 (offered Fall 2013): here.
  • Course website or Math 155 (offered Fall 2011 at Harvard): here.
  • Course website or Math 261y (offered Fall 2011 at Harvard): here.
  • Course website or Math 287x (offered Spring 2011 at Harvard): here.
  • Course website for Math 252x (offered Spring 2010 at Harvard): here.
  • Course website for 18.937 (offered Spring 2009 at MIT): here.
  • Course website for 18.915 (offered Fall 2008 at MIT): here.
  • Course notes for 18.917 (offered Fall 2007 at MIT): now available on OCW here.
  • Math Reviews (reviews not freely accessible)
  • Front for the xxx mathematics archives
  • 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. For selected older versions, go here

    Weil's Conjecture for Function Fields.
    A first draft of my joint work with Dennis Gaitsgory on the proof of Weil's Tamagawa number conjecture for function fields. (Strictly speaking, this is only "half" of the argument, but it's the more interesting half.) Last update: September 2014.
    pdf
    Higher Algebra.
    A newer version of my second book. Updated with some additional material on duality in monoidal infty-categories and Koszul duality for E_k algebras. Last update: September 2014.
    pdf
    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.
    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


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