The operad of framed formal curves and a program of Kontsevich

Abstract: It has long been conjectured (originally formalized by Kontsevich) that the operad of framed little disks can be enriched to an operad in an appropriate category of motives (in the sense of Grothendieck and Voevodsky). I will explain such a construction, in a motivic category associated to logarithmic schemes (or more generally, stratified formal schemes) and explain how (via ideas of Kontsevich, Tamarkin, Beilinson and others), this construction leads to a systematic resolution of several formality and deformation theoretic results, including the Deligne formality conjecture and deformation-quantization previously proven via more transcendental techniques.

algebraic topologycategory theoryquantum algebra

Audience: learners

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