EVENT DETAILS AND ABSTRACT

Title: Basics of deformation quantization of symplectic manifolds, II
Speaker: Boris Tsygan
Speaker Info: Northwestern
Brief Description: Learning seminar on microlocal methods in geometry
Special Note: Note unusual time
Abstract:

Abstract: I will define the metaplectic representation and Fourier integral operators in the formal setting.

Abstract of the series: I will start with some basics about differential operators, metaplectic representation, and Fourier integral operators in the context of formal power series. I will explain how this helps construct deformation quantization and some additional structure on a symplectic manifold (this proof of existence is in fact a combination of several known proofs). Later I will explain how to upgrade the category of modules over the deformed algebra to get something closer to the Fukaya category. I will also outline several parallels between this construction and the microlocal category of Dima Tamarkin.