06.11.2024, 14:00 - 16:00
– Campus Golm, Building 9, Room 2.22 and via Zoom
Institutskolloquium
Graphon Models for Inhomogeneous Random Graphs
Olga Klopp (Paris), Nicolas Verzelen (Montpellier)
Ada Masters (University of Wollongong)
Since Connes’s 1989 paper, the use of length functions to build spectral triples for group C*-algebras has become commonplace in noncommutative geometry. This construction, although sound at the level of quantum metric spaces, always gives rise to trivial K-homology. Using ingredients from geometric group theory, this can be remedied for many CAT(0) groups, including non-discrete groups. In the process, a novel group invariant from (quantum-group-equivariant) KK-theory is uncovered. The understanding of group extensions in this framework is a microcosm of the more general problem of the constructive unbounded Kasparov product. I will also touch on the problem of building spectral triples for crossed product C*-algebras arising from dynamical systems, using the Kasparov product and new tools inspired by conformal geometry.