# Workshop on Geometric Quantization (18w5182)

## Organizers

(Université de Montpellier)

(Université Paris Diderot - Paris 7)

Eckhard Meinrenken (University of Toronto)

## Description

The Banff International Research Station will host the "Workshop on Geometric Quantization" workshop from April 15th to April 20th, 2018.

Following the principle of quantum mechanics, the aim of geometric quantization is to associate to a classical phase space, described by a symplectic manifold $M$, a quantized version $Q(M)$ given by a Hilbert space. In this procedure, the Poisson bracket of functions on $M$, regarded as classical observables, should correspond to the commutator of self-adjoint operators, regarded as quantum observables. Furthermore, an action of a group $G$ by symmetries of $M$ should be implemented as a unitary representation on the quantum Hilbert space $Q(M)$. The philosophy of geometric quantization has been used in a variety of contexts, with remarkable and often surprising consequences. This workshop at BIRS will bring together mathematicians working on these topics and with different techniques such as topological K-theory, analytic estimates, $C^*$-algebras, representation theory. The philosophy of geometric quantization will act as a focal point for the interaction between all of these areas. The workshop will provide an excellent opportunity for experts working on different aspects of the theory to exchange ideas, leading to fresh insights and new developments.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).