报告题目：《QUANTISATION COMMUTES WITH REDUCTION》: A SURVEY

报告时间：2023-07-20  10:00-11:00

报告人：Prof. Xiaonan Ma, Universite Paris Cite

报告地点：理学院西北楼一楼报告厅

Abstract：Geometric quantization, introduced in the 1960's by Kostant and Souriau, gives a geometric method to properly quantize classical mechanical systems. The way in which symmetries of the classical systems are reflected in the quantization has been formulated into the principle that “quantization commutes with reduction”. We will review the idea “Quantization commutes with reduction”, or briefly, that “[Q,R]=0”, which first appeared as the famous Guillemin-Sternberg conjecture for compact symplectic manifolds. We will discuss our solution with Weiping Zhang on Vergne's conjecture in her ICM 2006 plenary lecture on noncompact symplectic manifolds, and our recent work with Hsiao and Marinescu, on the principle “quantization commutes with reduction” for Cauchy-Riemann (CR) manifolds.