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

Office: 2-271
Office Hours: Wednesdays, 4-5.
email: lurie
Department of Mathematics, MIT, Cambridge.

  • Course website for 18.915 (offered Fall 2008): here.
  • Course website for 18.937 (offered Spring 2009): here.
  • Course notes for 18.917 (offered Fall 2007): 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):

    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.
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    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.
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    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.
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    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).
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    An exposition of the Borel-Weil-Bott theorem on the cohomology of holomorphic line bundles over flag varieties.
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