Videos

Deformation Quantization I

Presenter
January 29, 2013
Keywords:
  • noncommutative algebraic geometry
  • D-modules
  • deformation quantization
  • derived categories
  • resolution of singularities
  • Hochschild cohomology
  • Kontsevich-Soibelman deformation theory
  • Grothendieck-Teichmuller group
MSC:
  • 13D09
  • 13D10
  • 13Dxx
  • 13-xx
  • 14Fxx
  • 14F05
  • 14F10
  • 14A22
  • 13D03
Abstract
In this mini-course, I will introduce the Hochschild cochain complex of an associative algebra A and show in what sense it ``governs'' formal deformations of A. I will discuss algebraic structures on the Hochschild complex and formulate Kontsevich's formality theorem. I will show how Kontsevich's formality theorem allows us to classify formal deformations of the algebra of functions on the affine space. If time will permit, I will say a few words about the description of formal quantization procedures in terms of the Grothendieck-Teichmueller group.