Seminar: (Gelfand's) Formal Geometry and the Algebraic Index Theorem
Niek de Kleijn will give a talk on (Gelfand's) Formal Geometry and the Algebraic Index Theorem.
Abstract: Formal Geometry provides a framework that links formal solutions of differential geometric problems to actual solutions. Solving the differential geometric problem formally means solving it at a point up to infinite order. We will give a description of the framework and some of the key results. Subsequently, we apply the construction to the problem of deformation quantization and the algebraic index theorem. This is an algebraic version of the Atiyah-Singer index theorem where one replaces the algebra of pseudo-differential operators by the deformation quantization of any symplectic manifold.
The lecture is part of the ALG/NCG/TOP Ph.D. students' seminar.