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


Algebra, Combinatorics & Optimization  C3: Momentum polytopes, string polytopes and generalizations  CupitFoutou, Heinzner, Littelmann, Reineke  Abstract: Actions of Lie groups by symplectic transformations are quite often Hamiltonian. By definition, this means that there exists an equivariant momentum map on the manifold with values in the dual Lie algebra of the acting group. In this project, we mainly focus on multiplicityfree manifolds (e.g. toric varieties, flag varieties and more generally spherical varieties), representation spaces of quivers and Nakajima quiver varieties. In the cases under study, the momentum map has remarkable convexity properties. One of our goals is to understand the images of these momentum maps in terms of the geometry of the varieties and vice versa.  Group:  
 PD Dr. Stéphanie CupitFoutou (PI)  mail: stephanie.cupit at rub.de  phone: 0234 / 32 23331  room: IB 3/95  Faculty of Mathematics  RuhrUniversity Bochum 
  Prof. Peter Heinzner (PI)  mail: peter.heinzner at rub.de  phone: 0234 / 32 23325  room: IB 3/115  Faculty of Mathematics  RuhrUniversity Bochum 
  Prof. Peter Littelmann (PI)  mail: peter.littelmann at math.unikoeln.de  phone: 0221 / 470 3715  room: 114  Mathematical Institute  University of Cologne 
  Prof. Markus Reineke (PI)  mail: markus.reineke at rub.de  phone: 0234/ 32 28241  room: IB 2/129  Faculty of Mathematics  RuhrUniversity Bochum 
  Daniel Schaefer (ds)  mail: d.schaefer at math.unikoeln.de  phone: 0221 / 470 4297  room: 212 (Weyertal 8690)  Mathematical Institute  University of Cologne 
  Tobias Waedt (ds)  mail: tobias.waedt at rub.de  phone: 0234 / 32 23330  room: IB 3/107  Faculty of Mathematics  RuhrUniversity Bochum 


