Geometric quantization (A03)

• Subject Area: Mathematics
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 281071066

The subject of this project is an in-depth study of geometric quantization from several vantage points, with the goal of strengthening and extending the quantum-classical correspondence. One aim is to generalize Berezin-Toeplitz quantization to new geometric contexts on symplectic manifolds. We shall also study the ergodic properties of geometric quantization in the semi-classical limit, especially for the sub-Riemannian Laplacian. In the framework of Hamiltonian Lie group actions, we will investigate to which extent the basic principle that "quantization commutes with reduction" remains valid beyond compact manifolds and compact groups.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 191: Symplectic Structures in Geometry, Algebra and Dynamics
• Applicant Institution: Universität zu Köln
• Co-Applicant Institution: Ruhr-Universität Bochum
• Project Heads: Privatdozent Dr. Alexander Alldridge, until 10/2016; Professor Dr. Peter Heinzner; Professor Dr. George Teodor Marinescu