Some results on the geometry of deformation quantization

11/05/2013 - 12:15pm
11/05/2013 - 1:10pm
Jeremy Pecharich (Pomona College)

A mathematically sound model for quantum mechanics as been sought since the discovery of quantum mechanics in the beginning of the 20th century. One possible model was discovered by Bayen et al. in the 1970s following work of Gerhard Hochschild and Murray Gerstenhaber on deformations of associative algebras. In short, what a physicist calls quantization, a mathematician would say deformation. We will give an introduction to the work of Hochschild and Gerstenhaber on associative algebras and the work of Kontsevich which solves the problem of finding an associative deformation, aka quantization, for a class of associative algebras important to physics, namely functions on a Poisson manifold. If time permits, I will discuss joint work with Kai Behrend and Barbara Fantechi on quantization and Donaldson-Thomas theory.

Mudd Science Library 126, Pomona College