Deformation quantization and applications.

Lecturer: Prof. Boris Tsygan

Abstract: In this mini-course I will define deformation quantization, state its main properties, and review its recent applications, mainly to microlocal methods in symplectic geometry. I will also formulate a conjecture generalizes the Atiyah-Singer index theorem. More precisely, this conjecture expresses as an integral not just the index of an operator, but the entire virtual space Ker(D)-coker(D) as a point in the algebraic K-theory spectrum.