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