RTG 2965/1: “From geometry to numbers: Moduli, Hodge theory, rational points”

The proposed research training group builds on our common vision in algebraic and arithmetic geometry,
on our broad and excellent expertise and on the successful track record in graduate education at
Humboldt University Berlin and Leibniz University Hannover.
Our guiding principle is the interplay between geometry and numbers. A first manifestation
of this idea is the fact that geometric objects can be assigned algebraic invariants and, in particular,
numbers, which often play an important role in classification. Examples are given by Betti and Hodge
numbers, by intersection numbers on moduli spaces, by Mordell-Weil ranks and by the number of
rational points. Another prominent connection is given by the fact that many basic number theoretic
questions, such as the solvability of a Diophantine equation, gives naturally rise to a geometric shape
whose properties govern the underlying arithmetic problem. Conversely, various arithmetic ideas and
methods have important applications in geometry, Hodge theory and moduli theory.
Our research program rests on three main pillars for which our PIs are leading experts. Together
they will form an excellent basis for successful training of early career researchers:
? A. Hodge theory and topology of algebraic varieties;
? B. Geometry and combinatorics of moduli;
? C. Arithmetic of moduli and rational points.