# Operads and Motives in Deformation Quantization

@article{Kontsevich1999OperadsAM, title={Operads and Motives in Deformation Quantization}, author={Maxim Kontsevich}, journal={Letters in Mathematical Physics}, year={1999}, volume={48}, pages={35-72} }

The algebraic world of associative algebras has many deep connections with the geometric world of two-dimensional surfaces. Recently, D. Tamarkin discovered that the operad of chains of the little discs operad is formal, i.e. it is homotopy equivalent to its cohomology. From this fact and from Deligne's conjecture on Hochschild complexes follows almost immediately my formality result in deformation quantization. I review the situation as it looks now. Also I conjecture that the motivic Galois…

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