Mathematics Münster

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).

I will discuss the phenomenon of collapsing for sequences of Riemannian manifolds whose volume tends to zero while curvature remains uniformly controlled, with particular emphasis on lower Ricci curvature bounds. Understanding the topology and metric structure of the limit spaces, and their relation to the original sequence of manifolds, is a subtle question that has attracted a great deal of attention over the years. I will begin with a brief overview of classical results in the setting of sectional curvature bounds, and then turn to the Ricci framework, including Ricci limit spaces and their synthetic counterparts. In contrast with the sectional curvature setting, collapsing under nonnegative Ricci curvature is much more flexible and can produce wilder limit spaces. I will conclude with a recent joint result with Qin Deng on the topological structure of two-dimensional collapsed limits. Most of the talk will be based on examples.

Part of the M²A²-2 : Mathematical Modeling and Analysis-2 Conference

Friday 24 July 2026:
Giuseppe Capriani, Benedikt Jost, Gunnar Kaib, Ivano Primi, Christoph Tenbrock


More information: Industry Day Poster

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.

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

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

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

A day for MM postdocs to prepare for the next step, exchange and connect with other postdocs on career-and maths-related matters.

(1) Research Statements and Proposals (with Eugen Hellmann and Angela Stevens) - A session on preparing a research statement for applications or proposals for grant applications or permanent positions: What is important, tips+tricks, which level of specificity is needed, ...

(2) Scientific Profile (with Shirly Geffen and Hendrik Weber) - A session on what is important in the postdoc profiling phase.

More information and registration in September....