C*-algebras of symmetries and their invariants

• Applicant: Professor Dr. Sven Raum
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 550184791

This project advances recent breakthroughs, such as the classification theorem, in C*-algebra theory, with a focus on C*-algebras associated to symmetries, and their invariants. Three research directions will be pursued, including the study of C*-algebras associated with single homeomorphisms and more general groupoids; Hecke C*-algebras, which are deformations of C*-algebras constructed from groups; and operator algebraic aspects of hyperbolic groups and dynamics. In addition to investigating the Elliott invariant, consisting of K-theory and traces, we will consider non-stable K-theory (stable rank) and equivariant bivariant invariants, such as Ext-theory and Kasparov's KK-theory. The Project aims to foster a thriving community of operator algebra experts in the Potsdam-Prague region.

• DFG Programme: Research Grants
• International Connection: Czech Republic
• Cooperation Partner: Dr. Karen Strung