CRC Geometry and Arithmetic of Uniformized Strucutres
The new CRC/TRR 326 will concentrate on the mathematical technique of uniformisation, which can be used to replace complicated geometric objects with simpler ones without changing the local structure. The original complexity is encoded in a suitable symmetry group, i.e. translated into another “language”. This approach opens up new pathways to study the original object. The research seeks to expand techniques of uniformisation and refine them for different challenges, with the aim of applying them to central geometric and arithmetical problems. In doing so, the CRC/TRR researchers from the universities in Frankfurt, Heidelberg, and Darmstadt hope to gain new insights into moduli spaces, amongst other things. Their findings could be relevant particularly in the context of Galois representations and automorphic forms. Prof. Dr Alexander Schmidt from the Mathematical Institute of Heidelberg University is co-spokesperson of the “Geometry and Arithmetic of Uniformized Structures” CRC/TRR, which is receiving DFG funding in the amount of approximately 11.2 million euros.