Groups and Geometry (GRG)

Symmetries play a central role in mathematics.
Considering the inherent symmetries of a mathematical object allows to reduce the complexity of mathematical research problems. This often leads to an interesting interplay between geometric structures on one hand and algebraic structures on the other.
The research group “Groups and Geometry” led by Anna Wienhard started at HITS in 2015 (in addition to her professorship at Heidelberg Unversity). The researchers investigate various mathematical problems in the fields of geometry and topology, which involve the interplay between geometric spaces, such as Riemannian manifolds or metric spaces, and groups, arising for example from symmetries, acting on them. A special focus lies on the study of deformations spaces of geometric structures, moduli spaces of bundles, and Lie groups and their discrete subgroups. Beyond their research in mathematics the group members were also interested in exploring possible interactions with other sciences.

In November 2022, group leader Anna Wienhard left HITS to become Director at the Max Planck Institute for Mathematics in the Sciences, Leipzig. In July 2023, she was named “HITS Fellow”, the highest distinction the Institute awards .