Forschungsfelder und Projekte

 Forschungsfelder

• Geometrische Gruppentheorie
• Nichtkommutative Geometrie
• Funktionalanalysis/Operatoralgebren
• Ergodentheorie von Gruppenoperationen
• Algebraische K-Theorie
• Reelle Algebraische Geometrie

Aktuelle Forschungsprojekte

• Homotopy groups of algebraic K-theory (joint with Guillermo Cortinas)

• Connes embeddings conjecture and embedability of particular groups

• About the geometry of spectahedra and RZ-polynomials (joint Tim Netzer)
• Metric geometry of the space of positive invertible operators on Hilbert space
• L²-invariants of groups and manifolds
• John von Neumann's continuous geometries - old and new
• Algebraic Geometry of topological spaces (joint with Guillermo Cortinas)
• G-equivariant Morse theory (joint with Matthias Schwarz)