Anton Khoroshkin (Higher School of Economics)
Around Deformation quantization
First, I will explain two different proofs of the existence of deformation quantization of the functions on the Poisson manifold due to M.Kontsevich and D.Tamarkin. Second I will explain the complexity of this problem and the equivalence of this two proofs. Third, I will introduce the Grothendieck-Teichmuller group and its action on the set of quantizations. Finally, I will translate everything to the language of operads and state the known and open questions around.
The talk is based on the works of Kontsevich, Tamarkin and Willwacher and their collaborators.
Thursday, 6 December 2018:
Friday, 7 December 2018:
Place : IMBM Seminar Room, Boğaziçi University South Campus
https://webusers.imj-prg.fr/~bernhard.keller/publ/emalca.pdf
Kontsevich, Maxim. "Deformation quantization of Poisson manifolds." Letters in Mathematical Physics 66.3 (2003): 157-216, https://arxiv.org/abs/q-alg/9709040
Loday, Jean-Louis, and Bruno Vallette. Algebraic operads. Vol. 346. Springer Science & Business Media, 2012.
http://irma.math.unistra.fr/~loday/PAPERS/LodayVallette.pdf
Lambrechts, Pascal, and Ismar Volić. Formality of the little 𝑁-disks operad. Vol. 230. No. 1079. American Mathematical Society, 2014, https://arxiv.org/abs/0808.0457
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The remaining part was not covered in the lectures
D.Tamarkin "Another proof of M. Kontsevich’s formality theorem", Preprint, https://arxiv.org/abs/math/9803025.
(not simple for reading)
https://arxiv.org/abs/0905.1789
Ševera, Pavol, and Thomas Willwacher. "Equivalence of formalities of the little discs operad." Duke Mathematical Journal 160.1 (2011): 175-206.
Willwacher, Thomas. "M. Kontsevich’s graph complex and the Grothendieck–Teichmüller Lie algebra." Inventiones mathematicae 200.3 (2015): 671-760.
Kontsevich, Maxim. "Derived Grothendieck–Teichmüller group and graph complexes [after T. Willwacher]." Séminaire Bourbaki (2017): 2016-2017, http://www.bourbaki.ens.fr/TEXTES/1126.pdf
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