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


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 numbertheoretic properties of integral polytopes, in particular reflexive polytopes. This connection allows us to use powerful tools coming from equivariant cohomology and Ktheory, 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 RodriguezVillegas about the position of their roots.  Group:  
 Prof. Kathrin Bringmann (PI)  mail: kbringma at math.unikoeln.de  phone: 0221 / 470 4334  location: Gyrhofstr. 8b  Mathematical Institute  University of Cologne 
  Prof. Silvia Sabatini (PI)  mail: sabatini at math.unikoeln.de  phone: 0221 / 470 2890  room: 8  Mathematical Institute  University of Cologne 
  Dr. Markus Schwagenscheidt (pd)  mail: mschwage at math.unikoeln.de  phone: 0221 470 1302  room: C 105 (Gyrhofstrasse 8a)  Mathematical Institute  University of Cologne 


