Vasily Dolgushev (Temple)
Exhausting quantization procedures
Deformation quantization is a procedure which assigns a formal deformation of the associative algebra of functions on a variety to a Poisson structure on this variety. Such a procedure can be obtained from Kontsevich's formality quasi-isomorphism and, it is known that, there are many homotopy inequivalent formality quasi-isomorphisms. I propose a framework in which all homotopy classes of formality quasi-isomorphisms can be described. More precisely, I will show that homotopy classes of ``stable'' formality quasi-isomorphisms form a torsor for the group $\exp(H^0(GC))$, where $GC$ denotes Kontsevich's graph complex. The group $\exp(H^0(GC))$ is isomorphic to the Grothendieck-Teichmueller group which is, in turn, related to moduli of curves, theory of motives, and the absolute Galois group of the field of rationals.