Symplectic Structures in Geometry, Algebra and Dynamics
Collaborative Research Centre TRR 191
 
A1, A2, A3, A5, A6, A7
B1, B2, B3, B4, B5, B6, B7
C1, C2, C3, C4, C5
Algebra, Combinatorics & Optimization
C4: Combinatorics of manifolds with symmetries and modularity properties
Bringmann, Sabatini
Abstract:
We use the correspondence between integral polytopes and symplectic toric manifolds to study combinatorial and number-theoretic properties of integral polytopes, in particular reflexive polytopes. This connection allows us to use powerful tools coming from equivariant cohomology and K-theory, as well as the rigidity and modularity properties of equivariant genera on toric varieties. We study the Hilbert and Ehrhart polynomials using this new approach, starting with the investigation of questions posed by Rodriguez-Villegas about the position of their roots.
Group:
 
Prof. Kathrin Bringmann (PI)
mail: kbringma at math.uni-koeln.de
phone: 0221 / 470 4334
location: Gyrhofstr. 8b
Mathematical Institute
University of Cologne
Prof. Silvia Sabatini (PI)
mail: sabatini at math.uni-koeln.de
phone: 0221 / 470 2890
room: 8
Mathematical Institute
University of Cologne
Impressum Institution of DFG, MI University of Cologne and FM Ruhr-University Bochum