Topology & Equivariant Theories 
A1, A2, A3, A5, A6, A7, A8

Dynamics & Variational Methods 
B1, B2, B3, B4, B5, B6, B7, B8

Algebra, Combinatorics & Optimization 
C1, C2, C3, C4, C5, C6, C7

MercatorFellow 
20172020


Topology & Equivariant Theories  A3: Geometric quantization  Heinzner, Marinescu  Abstract: The main idea in the theory of geometric quantization (introduced by Kostant and Souriau) of a manifold X is to associate with X "quantum" Hilbert spaces defined by means of some canonical geometric constructions. In the presence of a group action, an important metaprinciple is "reduction commutes with quantization". This principle describes how the quantization of the quotient relates to the quantization of the original manifold. We will consider the following aspects of quantization: (1) BerezinToeplitz quantization, (2) Holomorphic Morse inequalities, (3) Ergodic complex geometry, (4) Quantization and reduction. One of the tools employed will be Szegö and Bergman kernel expansions.  Group:  
 Prof. Peter Heinzner (PI)  mail: peter.heinzner at rub.de  phone: 0234 / 32 23325  room: IB 3/115  Faculty of Mathematics  RuhrUniversity Bochum 
  Prof. George Marinescu (PI)  mail: gmarines at math.unikoeln.de  phone: 0221 / 470 2661  room: 112  Mathematical Institute  University of Cologne 
  Dr. Nikhil Savale (pd)  mail: nsavale at math.unikoeln.de  phone: 0221 / 470 1303  room: C 107 (Gyrhofstr. 8a)  Mathematical Institute  University of Cologne 


