Institute of Algebra, Number Theory and Discrete Mathematics Institute News
New Research Training Group in Mathematics: From Geometry to Numbers

New Research Training Group in Mathematics: From Geometry to Numbers

© Ulrich Derenthal, Oliver Labs

The German Science Foundation (DFG) has greenlit the new Research Training Group (RTG) 2965, titled "From Geometry to Numbers: Moduli, Hodge Theory, Rational Points," hosted by Leibniz Universität Hannover (LUH) in partnership with Humboldt-Universität zu Berlin. The DFG has awarded 6.7 million Euros for this RTG. The program will kick off on October 1, 2024, and run in its first phase through September 30, 2029.

The RTG focuses on the fascinating connections between geometry and numbers. The goal is to uncover, describe, and understand new geometric objects and shapes that cannot be visualized — often neither by humans nor by computers. These shapes are frequently described by algebraic equations, some of which play an important role in theoretical physics. Even if the algebraic equations appear simple, the important geometric properties of the corresponding solution sets are often unknown. The goal of the RTG is to understand these solution sets and reveal the beautiful underlying geometry. An important principle is the idea that one can associate numerical invariants to geometric objects, for instance via counting points or special curves, by topological and Hodge theoretic means, or via combinatorial and moduli theoretical approaches.

Students admitted to this RTG will study an exciting blend of geometry, algebra, and number theory, and use this to push the boundaries of mathematical knowledge in these fields through their own research.

Leading this initiative are Prof. Dr. Stefan Schreieder from LUH (speaker) and Prof. Dr. Gavril Farkas from HU Berlin (co-speaker). At LUH, six researchers from two institutes are involved: Prof. Dr. Michael Cuntz (IAZD), Prof. Dr. Ulrich Derenthal (IAZD), Prof. Dr. Ziyang Gao (IAZD), Prof. Dr. Stefan Schreieder (IAG), Prof. Dr. Matthias Schütt (IAG), and Jun.-Prof. Dr. Isabel Stenger (IAG).

Together with the RTG 2965, a total of four Research Training Groups at LUH will be funded by the DFG in the future.