Christopher Douglas

I am a Research Fellow at the Miller Institute in Berkeley. My research is in algebraic and geometric topology. Lately I am thinking about geometric aspects of elliptic cohomology and about the structure of three- and four-dimensional topological field theories.
Together with my friends Andre Henriques, Mike Hill, and John Francis, I started the annual Talbot Workshops. These workshops have been supported by NSF Grants DMS-0512714 and DMS-0805838. The first workshop, in 2004, was on "Geometric Models for Elliptic Cohomology" and our plenary speaker was Stephan Stolz. David Ben-Zvi guided us through the 2005 workshop on "The Geometric Langlands Program". The 2006 workshop, mentored by Michael Weiss, focused on "Automorphism Groups of Manifolds". The 2007 workshop was about "Topological Modular Forms", with our very own Mike Hopkins. Most recently, Dennis Gaitsgory led the 2008 workshop on "Affine Lie Algebras and Chiral Structures." Here is the workshop homepage, which includes pictures and information about past workshops.

Here are some recent papers, and titles for papers being drafted:

  • Fusion Rings of Loop Group Representations: pdf or postscript

  • Homological Obstructions to String Orientations (with A. Henriques and M. Hill): pdf or postscript

  • Higher Topological Cyclic Homology and the Segal Conjecture for Tori (with G. Carlsson and B. Dundas): pdf or postscript

  • On the Structure of the Fusion Ideal, Commun. Math. Phys. (2009), to appear: pdf or postscript

  • Topological Modular Forms (book, with A. Henriques, M. Hill, and J. Francis). Sample chapter: "Sheaves in Homotopy Theory".

  • On the Twisted K-Homology of Simple Lie Groups, Topology 45 (2006), 955-988.: pdf or postscript

  • Trace and Transfer Maps in the Algebraic K-Theory of Spaces, K-Theory 36 (2005), 59-82.: for perusing (dvi) or downloading (ps)

  • On the Fibrewise Poincare-Hopf Theorem, Contemp. Math. 407 (2006), 101-111.: for perusing (dvi) or downloading (ps)

  • Twisted Parametrized Stable Homotopy Theory (thesis): pdf or postscript

  • Geometric String Structures (with A. Henriques), in preparation.

  • Conformal Nets II: Nets, Defects, Sectors, and Intertwiners (with A. Bartels and A. Henriques), in preparation.

  • Conformal Nets I: Symmetric Monoidal 3-Categories (with A. Bartels and A. Henriques), in preparation.

    • Here is a drawing of the Hasse diagram of the root system of E8. As described in the paper on Fusion Rings on the left, the diagram also encodes the generators of the fusion ideal of E8 at any level.

    Here is a picture of the real projective space of dimension 23. As described in the paper on String Orientations on the left, the picture shows that this manifold is string, but not 5-brane.

    In 2007 I taught two courses:

    The first was an undergraduate course in algebraic topology. Topics included the classification of surfaces, the fundamental group, covering spaces, knot theory, and basic homotopy theory.

    The second was a graduate literature seminar intended for students studying algebraic or geometric topology or symplectic, algebraic, or differential geometry, who had completed 282ABC or equivalent.

    As a counterpoint to my mathematical endeavors, I have been a contributing editor and cofounder of Topic. Topic (now in stasis) was a quarterly magazine publishing provocative nonfiction personal narratives (both literary and visual) about individual topics of contemporary interest. (War, Cities, Prisons, Food, Sin, and Music were the subjects of recent issues.) Our contributers are best characterized by example: a professor of landscape architecture, a man serving a life sentence for murder, an American submarine builder, a Nobel laureate for peace, a cook in a state penitentiary, a Malawian bishop, an English Civil War recreator, an Azerbaijani relief worker, and so on. Here are sample images from the print edition. 
    Christopher Douglas
cdouglas@math.berkeley.edu

Department of Mathematics
University of California
Berkeley, CA 94720