Termine

A complex valued function $f:(M,g) \to \C$ is said to be a $(\lambda,\mu)$-eigenfunction if it is eigen with respect to both the Laplace-Beltrami operator and the conformality operator $\kappa(f,f) = g(\nabla f,\nabla f)$. Recent developments have shown that $(\lambda,\mu)$-eigenfunctions can be used in the construction of harmonic morphisms, proper r-harmonic maps, and minimal submanifold of codimension two. There has also been interest in classifying eigenfunctions. In this talk we consider the case when (M,g) is a compact Lie group equipped with a bi-invariant metric, as the Laplace-Beltrami operator's spectral theory is described by the Peter-Weyl theorem. We use the Peter-Weyl theorem, and other representation theoretic techniques in order to classify all the pairs $(\lambda, \mu)$ as well as describe conditions which ensure the existence of eigenfunctions. Finally, we produce new eigenfunctions on both compact Lie groups G and Riemannian symmetric spaces G/K. This is a joint project with Oskar Riedler. If you are interested please contact Prof. Dr. Anna Siffert (asiffert@uni-muenster.de)

Partial group actions on spaces by homeomorphisms between open sets provide a rich class of C*-algebras via the crossed product construction. We start an in-depth investigation when a general Hausdorff étale groupoid is a transformation groupoid by a partial action. Our negative results contain the first examples of Hausdorff étale groupoids which do not arise as transformation groupoids of partial group actions and which are not inner amenable in the sense of Anantharaman-Delaroche. On the positive side, we prove that many higher rank graph algebras as well as many unital UCT Kirchberg algebras can be realized via partial group actions. This is joint work with Alcides Buss.

Kolloquium über Geschichte und Didaktik der Mathematik

via zoom If you are interested please contact Prof. Dr. Anna Siffert (asiffert@uni-muenster.de)

Benjamin Brück and Michael Wiemeler will talk about their Habilitation. Margarete will give a Departure Talk.

Further information

We introduce command-line assistants as LLM-based systems that can do real work through tools, permissions, and sandboxed execution environments. We explain how these assistants differ from plain chatbots, opening new possibilities but also introducing challenges and risks.

The main focus is on existing and possible applications in our department.

In this talk we investigate the Fröhlich polaron in the strong coupling limit, which is a model describing the interactions of a charged particle, e.g. an electron, with a polarizable environment. Notably, the model is simple enough to allow for rigorous mathematical proofs, while giving rise to a multitude of interesting and non-trivial phenomena, such as an effectively increased mass of the electron. In particular, we will discuss the Landau-Pekar formula for the effective mass of the Fröhlich polaron from an functional analytic (variational/ operator based) view point.