Hengstberger Award Prize winner 2025
Groups that act on non-positively curved spaces
Non-positively curved (NPC) spaces are mathematical objects that are ubiquitous in nature and in our everyday life experience. Flat Euclidean spaces are probably the most common examples.
This is not all: negatively curved objects shape, for example, the head of lettuce or a tree canopy. Wrinkles, curls and fractal behaviours – given by the negative curvature – have crucial biological advantages. Recent advances in machine learning have also revealed that (isometric) embeddings of neural networks in higher-dimensional negatively curved spaces have key implications in language learning.
NPC spaces also play a leading role in several areas of pure mathematics. The workshop primarily focuses on their role in geometric group theory, a young yet rapidly growing area lying at the intersection of algebra and geometry. A key problem is to understand suitable collections of symmetries, called “groups”, of the relevant spaces. From spaces, one can deduce algebraic properties of their groups of symmetries, as well as transfer concepts (curvature, large-scale properties, …) to groups, with key classification advantages. The workshop focuses on two aspects in this direction: approximating groups of symmetries of NPC spaces via discrete substructures (lattices) and studying the finiteness properties of the relevant groups. The workshop brings together young and established researchers with the goal of sharing recent developments and future directions around the two themes above, as well as promoting new synergies.
Dr. Bianca Marchionna
Institut für Mathematik
Mathematikon
Im Neuenheimer Feld 205
69120 Heidelberg
b.marchionna@mathi.uni-heidelberg
Veranstaltungstermin: 15.06.- 18.06.2026