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Abstrakt: Scalar curvature is a very weak and flexible local invariant in Riemannian geometry. So it is surprising that coupling lower scalar curvature bounds with seemingly harmless topological conditions can recover very powerful rigidity statements, such as Llarull?s theorem or the positive mass theorem. In this talk I will begin by introducing some aspects related to the comparison geometry of lower scalar curvature bounds, focussing in particular on Llarull?s theorem. After this I will discuss a recent rigidity theorem in this setting. This is joint work with Thomas Tony.

Cartan subalgebras in operator algebras have been an active research area since their introduction in the 1970s (by Vershik and Feldman-Moore for von Neumann algebras, and Renault and Kumjian for C*-algebras). While on the side of von Neumann algebras some deep rigidity results have been established, much less is known about the variety of Cartan subalgebras that a C*-algebra can admit, with only a few exceptions of certain subhomogeneous C*-algebras. In this talk, we discuss another case of C*-algebras whose Cartan subalgebras can be parametrized in full, namely unital essential extensions of continuous functions on the circle by the compact operators (which includes the Toeplitz algebra). As we shall see, in the non-trivial extension case, these C*-algebras admit no C*-diagonals, all of their Cartan subalgebras have the one-point compactification of the natural numbers as their spectrum, and, up to conjugacy, these are parametrized by certain "near symmetries" of the natural numbers. This is joint work with Philipp Sibbel.

We invite all early career researchers who have started their position at Mathematics Münster in 2026 to join us for a welcoming Meet&Greet session with the Cluster spokespersons, some investigators, the MM management staff and all the new members.

We invite all doctoral researchers who have started their position at Mathematics Münster since January 2026 to join us for this MM Spotlight. Learn more about how to start into the doctoral research, what the mentoring programme is all about and get to know your fellow new colleagues.