Kontsevich's Deformation quantization of Poisson manifolds

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


  • 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