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The elliptic genus of a singular variety

Thursday 12th December 2002 - 16:30 to 17:30
INI Seminar Room 1
Session Title: 
Elliptic cohomology and chromatic phenomena
I will begin by describing how the elliptic genus of a manifold can be characterised among all characteristic numbers by its "rigidity" properties. Next, I will give my characterization of (one version of) the elliptic genus by its invariance under "flops", a class of surgeries that comes up naturally in algebraic geometry. Borisov and Libgober proved a stronger invariance property, which allowed them to define the elliptic genus for a large class of singular complex spaces. To find even stronger invariance properties of the elliptic genus, we can try to define the elliptic genus for singular real spaces; I will discuss some calculations which support this possibility.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons