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

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Algebra, Combinatorics & Optimization  C4: Combinatorics of manifolds with symmetries and modularity properties  Bringmann, Sabatini  Abstract: The goal of this project is, on the one side, to study the implications  at a geometric and number theoretical level  of the rigidity and vanishing of certain elliptic genera associated with an almost complex manifold acted on by a circle, which will give results in the direction of the Mukai conjecture. On the other side we will define elliptic genera for combinatorial objects, such as cones and abstract GKM graphs, and generalize related results by Borisov and Gunnels for the socalled toric modular forms.  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 


