Welcome to the website of the division "Geometry, Groups, and Dynamics" at the Max Planck Institute for Mathematics in the Sciences in Leipzig.
We conduct fundamental research in geometry, group theory, and dynamics, explore applications and interactions with other sciences and engage in communicating mathematics to the broader public.
An important key concept in our work is symmetry, captured in the mathematical notion of symmetry groups. We investigate actions of symmetry groups on topological spaces or Riemannian manifolds.
Our research focus lies in the areas of discrete subgroups of Lie groups, symmetric and homogeneous spaces, moduli spaces of geometric structures, geometry and dynamics of representation varieties, Anosov representations, higher Teichmüller theory, positivity in Lie groups, cluster algebras, and Higgs bundles. We also explore applications of geometry and topology in other sciences.
Of particular interest for us are, on the one hand, interactions with theoretical physics, in particular, the study of quantum field theories, and on the other hand, applications of geometric and topological methods in data analysis and machine learning.