Kontsevich's Deformation quantization of Poisson manifolds

Outline:

• Physical motivation: deformation quantization, Moyal star product
• The main problem: classification of star products
• Kontsevich formula for the star product
• dg Lie algebras and $L\sub{\infty}$-algebras
• Two dg Lie algebras: the multivector fields and the multidifferential operators
• The Hochschild-Konstant-Rosenberg theorem
• The formality map: graphs and compactification of configuration spaces
• Sketch of proof

References:

• Kontsevich M, Deformation Quantization of Poisson manifolds, Lett. Math. Phys. 66 (2003) 157.
• Cattaneo A S, Formality and star products. Lecture notes taken by D. Indelicato, London Math. Soc. Lecture Note Ser. 323 (2005) 79–144.
• Gutt S, Deformation quantisation of Poisson manifolds, Geom. Topol. Monogr. 17 (2011) 171-220.