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Complex orientations and Motivic Galois theory

Friday 13th December 2002 - 10:00 to 11:00
INI Seminar Room 1
Session Title: 
Elliptic cohomology and chromatic phenomena
Grothendieck's program for an anabelian geometry suggests that the Galois group Gal(Q=Q) possesses very interesting pronilpotent representations, associated to a free Lie algebra on generators conjecturally identied with the values of the zeta function at odd positive integers > 1. Some such automorphism algebra acts on Kontsevich's deformation quantization of Poisson manifolds, and there are rea- sons for thinking there are similar actions on algebras of asymptotic expansions for geometric heat kernels [math.SG/9908070] dened via Ginzburg's cobordism of symplectic manifolds. This is all pretty hypothetical, but there is an interesting concrete representa- tion of such a free Lie algebra in the group of formal dieomorphisms of the line, closely related to a genus associated to the Gamma function by Kontsevich [math.QA/9904055, x4.6]; it is a deformation of the A^-genus, connected to the the- ory of quasisymmetric functions [math.AG/9908065]. This genus seems to be worth investigating, whether one believes any of the conjectures above, or not; this talk is an introduction to its properties. 1
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons