Distinguished Lecture——《QUANTISATION COMMUTES WITH REDUCTION》: A SURVEY
报告人：Prof. Xiaonan Ma (Universite Paris Cite)
时间：2023-07-12 15:00-16:00
地点：理科一号楼1114
摘要：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.
个人简介：麻小南, 现为巴黎西岱大学教授，国际数学家大会(ICM) 45分钟报告者。麻小南的主要研究领域为微分几何、复几何以及拓扑。他尤其专注于流形上的指标理论以及整体分析的研究，主要研究eta不变量和解析挠率的解析、微分-拓扑性质，椭圆亏格，Bergman核，几何量子化以及相关课题。麻小南与张伟平曾运用解析局部化的思想和技巧，解决了法国科公司院士维尔格尼提出的非紧空间上的几何量子化猜想。麻小南曾多次获得国际大奖：2006年获西班牙Ferran Sunyer i Balaguer奖；2017年获法国科公司Sophie Germain大奖；2022年获德国Gay-Lussac-Humboldt 奖。
