Algebra and Mathematical Physics seminar.
The speaker, Marvin Dippell from the University of Salerno, will give a gentle introduction to Deformation Quantization and Reduction (10:00 - 10:45) followed by a more specialized seminar (11:00 - 11:45).
Abstract:
The first part of this talk will be an introduction to formal deformation quantization. I will introduce star products as a way to quantize a given classical mechanical system by deforming the pointwise product of the commutative algebra of smooth functions on a Poisson manifold. We will study the deformation theory of this algebra by means of its Hochschild cohomology, leading us to the well-known Hochschild-Kostant-Rosenberg theorem.
In the second part I will present a framework for incorporating (symmetry) reduction into deformation quantization. To this end we will consider so called constraint algebras and explore their deformation theory using a modification of Hochschild cohomology. In the end I will present first results on the way to an Hochschild-Kostant-Rosenberg theorem which is compatible with reduction.