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

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

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

MercatorFellow 
20172020


Dynamics & Variational Methods  B4: Loop groups and the path model  Littelmann, Lytchak  Abstract: The project intends to give a geometric reinterpretation of the combinatorial path model in representation theory. The aim is to merge various points of view on the geometric and topological construction of bases of representations of semisimple Lie algebras and their associated combinatorial models. One of these points of view is symplectic; it is based on the study of MirkovićVilonen polytopes, which characterize one such basis and arise as the image under the momentum map of the relevant basis. Variational methods enter via Morse theory on loop groups.  Group:  
 Prof. Peter Littelmann (PI)  mail: peter.littelmann at math.unikoeln.de  phone: 0221 / 470 3715  room: 114  Mathematical Institute  University of Cologne 
  Prof. Alexander Lytchak (PI)  mail: alytchak at math.unikoeln.de  phone: 0221 / 470 2888  room: 109  Mathematical Institute  University of Cologne 
  Valentin Rappel (ds)  mail: vrappel at math.unikoeln.de  phone: 0221 / 470 4297  room: 212  Mathematical Institute  University of Cologne 


