Harmonic analysis on compact groups and quantization
Speaker:Prof. José Cidade Mourão
Associate Professor
Universidade Técnica de Lisboa
Date & Time:14 Feb 2014 (Friday) 10:30
Venue:ILG127
Organized by:Department of Mathematics

Abstract

Segal-Bargmann unitary transforms for a compact Lie group K are unitary maps from L^2 spaces of functions on K to spaces of holomorphic L^2 functions on the complexification K_C of K. We will describe the relation of these transforms with complex time evolution in geometric quantization. Certain aspects of the large N limit of the Segal-Bargmann transform for the unitary group U(N) and relations with the large N limit in random matrices will be reviewed.

Biography

Prof. José Cidade Mourão is currently an Associate Professor at the Mathematics Department of Instituto Superior Técnico at Universidatd Técnica de Lisboa. Prof. Mourão obtained his Ph.D. in Physics and Mathematics by the State University of Moscow. The publications of Prof. Mourão include, Complex time evolution in geometric quantization and generalized coherent state transforms, Quantization of some moduli spaces of parabolic vector bundles on CP1, Toric Kähler metrics seen from infinity, quantization and compact tropical amoebas, Quantization of Abelian Varieties: distributional sections and the transition from Kähler to real polarizations, On the BKS Pairing for Kähler Quantizations of the Cotangent Bundle of a Lie Group etc.