Dr. Martin Lüdtke

Research Interest

I am working in arithmetic geometry, and more specifically in anabelian geometry. In this field, which is based on conjectures of Grothendieck, one studies the geometry and arithmetic of schemes from the viewpoint of their étale fundamental groups. The section conjecture predicts a group-theoretic description of rational points in terms of the fundamental group. In my doctoral dissertation, I studied the section conjecture for curves over p-adic fields and showed that it holds for certain intermediate cases between the birational case, which is known due to Koenigsmann, and the full curve, where the conjecture is still open. I am also interested in non-abelian Chabauty and have worked on explicit applications to the S-unit equation.