Symplectic Structures in Geometry, Algebra and Dynamics
Collaborative Research Centre TRR 191
 
A1, A2, A3, A5, A6, A7, A8
B1, B2, B3, B4, B5, B6, B7, B8
C1, C2, C3, C4, C5, C6, C7
2017-2020
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 meta-principle 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) Berezin-Toeplitz 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
Ruhr-University Bochum
Prof. George Marinescu (PI)
mail: gmarines at math.uni-koeln.de
phone: 0221 / 470 2661
room: 112
Mathematical Institute
University of Cologne
Dr. Nikhil Savale (pd)
mail: nsavale at math.uni-koeln.de
phone: 0221 / 470 1303
room: C 107 (Gyrhofstr. 8a)
Mathematical Institute
University of Cologne
Maxim Kukol (ds)
mail: maxim.kukol at rub.de
phone: 0234 / 32 25681
room: IB 3/105
Faculty of Mathematics
Ruhr-University Bochum
Christian Zöller (ds)
mail: christian.zoeller at rub.de
phone: 0234 / 32 23324
room: IB 3/117
Faculty of Mathematics
Ruhr-University Bochum
Impressum Institution of DFG, MI University of Cologne, FM Ruhr-University Bochum and MI University of Heidelberg