Mathematics Münster

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.

My talk shall be concerned with the problem of rigorous derivation of the macroscopic laws governing heat propagation from the microscopic models formulated in statistical mechanics. A classical microscopic model of the thermal energy transport is provided by a chain of coupled oscillators on the integer lattice, that describes atoms (or molecules) in a crystal. Establishing, in a mathematical precise way, such laws, by taking appropriate scaling limits, is the central problem of rigorous statistical mechanics. One of the tools used to conclude such results is to introduce some stochasticity inside the system. We summarise some of the results obtained recently concerning the derivation of the macroscopic heat equation from the microscopic behaviour of a harmonic chain with a stochastic perturbation. We focus our attention on the emergence of macroscopic boundary conditions. The results have been obtained in collaboration with Joel Lebowitz, Stefano Olla and Marielle Simon.

YAM Fellows present their research with David Jean Baptiste Bilong, Gilles Jordan Pedieu Tcheuha, and Miarisoa Elalie Rasamimanana.

More information on the YAM Fellowship Programme...

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.

Tosio Kato's monumental work on perturbation theory of operators was highly motivated by applications to partial differential equations in non homogeneous media. For example, how is the propagation of waves affected by perturbation of its conductivity? The first attempts in the fifties were by functional analysis methods because it is expected that kinetic energy is related to spectrum. But they were not successful. The connection to harmonic analysis questions was made by A. McIntosh in the eighties. A complete solution occurred in the early 2000 and still implies nowadays unsuspected consequences. This talk will present some aspects of this story.

Extremal black holes are special solutions to the Einstein field equations characterized by maximal spin or charge relative to their mass. In the celebrated thermodynamic analogy of black hole mechanics, they are distinguished by having exactly zero temperature. In this talk, I will present a proof showing that extremal black holes can form dynamically from gravitational collapse rather than appearing only as inaccessible limiting objects in parameter space. I will then introduce a series of recently formulated conjectures, together with partial results, that aim to clarify the role of extremal black holes in gravitational collapse, their connection to threshold phenomena, and critical behavior in black hole formation. This talk is based on joint work with Y. Angelopoulos (BIMSA) and R. Unger (UC Berkeley).