Collaborative Research Center GAUS starts

Geometry and Arithmetic of Uniformized Structures

8 July 2021
SFB 326 - GAUS startet mit Eva Viehmann als Principal Investigator

Structural questions in geometry and arithmetic - that is what mathematicians want to answer in the Collaborative Research Center Transregio (CRC TRR) 326 "Geometry and Arithmetic of Uniformized Structures (GAUS)". GAUS will start in July 2021 and will be funded by the German Research Foundation (Deutsche Forschungsgesellschaft - DFG) with 9.2 million euros over the next four years.

The research center, which is based in theoretical mathematics, is coordinated by Goethe University Frankfurt. Other participating institutions are the Technical University of Darmstadt and the University of Heidelberg, as well as the Johannes Gutenberg University of Mainz and the Technical University of Munich (TUM) as associated institutions. Here, Eva Viehmann, TUM Professor of Arithmetic Geometry, is represented as Principal Investigator.

Geometry and Arithmetic of Uniformized Structures

In the DFG collaborative research center TRR 326 GAUS, mathematicians are working on the uniformization of very complicated geometric spaces. The concept of uniformization goes back to ideas of Felix Klein and Henri Poincaré from the 19th century. The basic idea of uniformization is to replace complicated geometric objects with simpler ones while preserving the local structure. The original mathematical complexity is encoded in an appropriate symmetry group.

New perspectives on geometric and number theoretic questions

Uniformization thus enables a translation of complexity into another "language". This opens up new perspectives on the original mathematical objects. The group wants to use this to investigate the geometry and arithmetic of algebraic varieties. The researchers try to identify fundamental connections, for example to moduli spaces and automorphic forms, Galois representations or cohomological structures.

For information on the research content, participants, offers and open positions in the Collaborative Research Center "Geometry and Arithmetic of Unified Structures", please visit the website CRC 326 – GAUS.