There’s a beautiful survey paper about elliptic cohomology that Jacob Lurie, an AIM 5-year fellow in the math department at Harvard, has recently put on his home page. This paper has been discussed a bit already by David Corfield and by Urs Schrieber.
I don’t have time right now to try and write up something comprehensible about those parts of the elliptic cohomology story that I kind of understand, and in any case I want to spend more time reading Lurie’s paper. It brings into the elliptic cohomology story several of my favorite pieces of mathematics (Atiyah-Segal completion, Freed-Hopkins-Teleman), in a way that I don’t yet understand. But in any case there’s a lot of very beautiful and very new mathematics in this paper, mathematics that has tantalizing relations to quantum field theory.
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