Testbrett

In der Hittorfstraße liegt möglicherweise ein ?Blindgänger? aus dem Zweiten Weltkrieg. Experten werden den Verdachtspunkt am 6. Mai (Mittwoch) vormittags freilegen. Ob eine Entschärfung und damit auch eine Evakuierung im Umfeld erforderlich ist, wird sich erst nach der Öffnung des Verdachtspunktes klären. Sollte eine Entschärfung erforderlich sein und das Gebiet im Umkreis von 250 Metern evakuiert werden müssen Aus diesen Grund ist unser Hotlinebüro in der Einsteinstr. an diesem Tag vor Ort nicht besetzt. Unsere anderen Hotlinebüros übernehmen die Schichten.

In this talk, I will begin with the classical isoperimetric inequality for closed curves in Euclidean space and its connection to the Plateau problem, as resolved by Douglas and Radó. The notion of non-positive curvature naturally enters the picture via the Gauss equation, which links the intrinsic and extrinsic geometry of surfaces. We then explore the relationship between the isoperimetric inequality and the intrinsic geometry of minimal discs. From there, the discussion extends beyond Euclidean ambient spaces to those of non-positive curvature, and from curves to higher-dimensional cycles. This talk includes results from joint work with Cornelia Druţu, Urs Lang, Alexander Lytchak, Panos Papasoglu, and Stefan Wenger.

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.

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

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.

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.

tba

tba