USAG

Uniformized Structures in Arithmetic and Geometry

The LOEWE research unit "Uniformed Structures in Arithmetic and Geometry" aims to gain new insights into current arithmetic and geometric classification problems by combining different techniques of uniformization.

This research unit bundles the broad expertise of TU Darmstadt and GU Frankfurt in the fields of number theory and arithmetic/algebraic geometry.

Our research program focusses on the following three areas:

Special Subvarieties
Automorphic Forms
Variation of Geometry

In research area A we explore Orthogonal Shimura Varieties and the Kudla Conjecture, in research area B we investigate Borcherds-Products as well as Vertex Algebras, and in research area C we study the Uniformization of Spherical Varieties, the Anabelian Section Conjecture, as well as Tropical Moduli Spaces.

The research areas A, B, and C are mutually interconnected and techniques of uniformization are crucial in our research approaches.