Wednesday, May 10th, 2017
11:00am - 12:00pm, in McCormack 2-207

Mark Hamilton

Mount Allison University, Canada

Independence of polarization in geometric quantization

Abstract: "Quantization," broadly speaking, is a method to go from a classical mechanical system to a "quantum" description of the same system. There are many methods of quantization; geometric quantization uses the geometry of the classical system (as the name suggests) to define the quantum version, and leads to surprising connections with algebraic geometry and representation theory. One of the necessary ingredients in geometric quantization is the choice of a "polarization," and a natural question is how much the result depends on this choice. A priori one might expect the dependence to be strong; on the other hand, physical intuition suggests that the result should be more or less independent of the choice, a fact that is borne out in many examples. In this talk I will explain the basics of geometric quantization and how the choice of polarization fits into the construction. I will review the main known examples showing "independence of polarization" - type phenomena, and discuss some recent techniques for connecting the quantizations resulting from different choices. Finally, I will describe recent work showing that "independence of polarization" holds in considerable generality.