Momentum polytopes, string polytopes and generalizations (C03)

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

The central theme of this project is the characterization, identification and variation of momentum polytopes for compact Lie group actions on symplectic spaces and related polytopes associated to actions of real reductive groups. The focus will lie on Lie group actions on spherical varieties, cluster varieties and more generally on Kählerian manifolds. A notable cross-sectional theme in this project is the study of flat degenerations. Important instances to be studied are the variations of momentum images in flat families, degenerations of spherical varieties to flag varieties via a moduli approach, and toric degenerations via the cluster variety approach.

• 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: Professorin Dr. Stéphanie Cupit-Foutou; Professor Dr. Peter Heinzner; Professor Dr. Peter Littelmann; Professor Dr. Markus Reineke