### Kontsevich's Deformation quantization of Poisson manifolds

Seminar course for the Master in Mathematical Physics, Amsterdam University, Fall 2015.

#### 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