Geometric Structures in Group Theory

Journal article

The general subject of the conference was geometric group theory, that is the study of groups via suitable actions on spaces endowed with additional structures, for instance a distance, a measure (class), or both of them with natural compatibilities. The interactions with other mathematical fields such as algebraic topology (e.g. via homological methods), functional analysis (e.g. via the theory of operator algebras), probability theory (e.g. via random walks) or even representation theory and number theory, play an increasing role in the development of this part of group theory.

Authors: Bridson, MR; Druţu, C; Kramer, L; Rémy, B

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: European Mathematical Society - EMS - Publishing House
• Journal: Oberwolfach Reports
• Volume: 22
• Issue: 1
• Pages: 275-338
• Publication date: 2025-08-29
• DOI: 10.4171/owr/2025/6
• EISSN: 1660-8941
• ISSN: 1660-8933
• Language: English
• Keywords: Topology (electrical circuits); Group representation; Combinatorics; Computer science; Probability theory; Algebraic structure; Artificial intelligence; Algebra over a field; Representation theory; Mathematics; Physics; Group theory; Group action; Pure mathematics; Group (periodic table); Class (philosophy)