How is it possible to simplify complicated geometrical and arithmetical shapes by means of uniformisation? The “Uniformised Structures in Arithmetic and Geometry“ (USAG) LOEWE cluster, which is being funded by the Hesse research support programme, has been tackling this research issue since 2018. Eleven new special research fields have now been approved by the German Research Foundation (DFG). One of them, the Transregio “Geometry and Arithmetic of Uniformised Structures (GAUS)” special research field (TRR 326 GAUS), is receiving funding worth EUR 9.2 million for four years and is linking up with the work of the LOEWE cluster.
Mathematicians working in TRR 326 GAUS are dealing with the uniformisation of particularly complicated geometrical shapes – this involves modern geometrical concepts, particularly tropical and p-adic types of geometry – and with similar applications for using the uniformisation technique with number theory issues. The research scientists are looking for fundamental interconnections, for example, with modular spaces, automorphic shapes, Galois modules and cohomological structures.
The Technical University of Darmstadt and the University of Heidelberg have successfully applied to be part of the TRR 326 in addition to the coordinating Goethe University in Frankfurt. The Johannes Gutenberg University in Mainz and the Technical University of Munich are associated partners. Professor Jakob Stix from the Goethe University in Frankfurt is the spokesperson for the special research field. Mathematics Professor Jan Hendrik Bruinier from the Technical University of Darmstadt, the spokesperson for the USAG LOEWE cluster, and Professor Alexander Schmidt from the University of Heidelberg are co-spokespersons.