Mathematics Münster

We invite all early career researchers who have started their position at Mathematics Münster since January 2026 to join us for this MM Welcome Event. Learn more about the Cluster, its research topics and opportunities. Get to know your fellow new colleagues.

Spectra arise in almost all parts of mathematics, and often they reflect some essential information from an underlying category. Examples are: the spectrum of prime ideals of a commutative ring, the spectrum of (indecomposable) injective objects in a Grothendieck category, the Ziegler spectrum arising in the model theory of modules, and last but not least the Balmer spectrum of a tensor triangulated category. The talk will provide a survey about these spectra from a representation theory perspective, with a special focus on their interplay.

Over the past decades, infinite-dimensional Riemannian geometry has developed into a vibrant area of research. Interest in the field has been driven by its emergence in a wide range of applications, notably in geometric data science, mathematical shape analysis, and geometric hydrodynamics. Although the fundamental definitions of Riemannian geometry extend almost effortlessly to infinite-dimensional spaces, many classical results from the finite-dimensional theory are known to fail in the infinite setting. In this talk, I will survey several phenomena unique to infinite dimensions and discuss conditions under which certain finite-dimensional properties can be partially recovered, including the non-degeneracy of the geodesic distance and Hopf-Rinow-type results. While the results will be illustrated using simple examples modeled on spaces of sequences, I will also discuss applications to the aforementioned areas of mathematical shape analysis and geometric hydrodynamics.

Get an insight into the research of five new postdoctoral researchers of Mathematics Münster. In short scientific presentations they will introduce their topics.
After the talks, there will be the opportunity to exchange ideas while enjoying tea, coffee and cake in the Common Room.

• Catrin Mair, Homotopy theory in a condensed world
• Stefan Schrott, Optimal transport of stochastic processes
• Mathias Sonnleitner, Connecting and separating dots
• Ferdinand Wagner, Habiro Cohomology & Refined THH
• Alexander Van Werde, On the spectral determinacy of random graphs

For any prime $p$, a finite group has as many irreducible complex characters of degree prime to $p$ as the normalizer of a Sylow $p$-subgroup. This equality, conjectured by John McKay in 1971, was reduced in 2007 by Isaacs--Malle--Navarro to a conjecture on representations of finite simple groups. Thanks to their classification we know that the latter are essentially finite groups of Lie type. Deligne--Lusztig theory helps to prove the McKay conjecture by this approach. For groups of characteristic different from $p$, the normalizers of Sylow $p$-subgroups belong to a larger class of subgroups related to parabolic subgroups of the ambient algebraic group for which Deligne-Lusztig varieties and induction functors have been used in the 1990s to provide a substitute to parabolic induction. This works well for unipotent characters. An important step is the construction of a Jordan decomposition of characters which is equivariant with respect to automorphisms of the simple group.

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5 sessions on professional competences. You can pick and choose: either one, several, or all sessions.
Open to all! All sessions are open to all MM researchers of Mathematics Münster, regardless of their experience level, as all input and exercises are designed for individual needs.
Register via: mm.careers@uni-muenster.de