Project Details
Projekt
Combinatorics of manifolds with symmetries and modularity properties (C04)
Subject Area
Mathematics
Term
since 2017
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 281071066
Elliptic genera of a certain level are modular forms associated with almost complex manifolds that encode much information about certain invariants of the manifold. If the latter admits a circle action preserving the almost complex structure then, according to celebrated theorems of Hirzebruch, Taubes and Bott-Taubes, some of them satisfy a key property known as "rigidity". 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, 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 so-called toric modular forms.
DFG Programme
CRC/Transregios
Applicant Institution
Universität zu Köln
Project Heads
Professorin Dr. Kathrin Bringmann; Professorin Dr. Silvia Sabatini
