Termine

In Kähler Geometry, the Yau?Tian?Donaldson Conjecture relates the differential geometry of compact Kähler manifold with an algebro-geometric notion called K-stability. I will start with a brief overview of the topic, and then I will discuss a possible non-Archimedean approach to solve this conjecture, generalizing a result of Chi Li to the transcendental setting.

The talk will discuss two aspects of gravitational instantons: mode stability of gravitational instantons, and T²-symmetric (toric) gravitational instantons. First, I will discuss Ricci-flat perturbations of gravitational instantons of Petrov type D. Analogously to the Lorentzian case, the Weyl curvature scalars of extreme spin weight satisfy a Riemannian version of the separable Teukolsky equation. As a step toward infinitesimal rigidity of the type D Kerr and Taub-bolt families of instantons, I will discuss the main ideas behind the proof of mode stability, that is, the fact that the Teukolsky equation admits no solutions compatible with regularity and asymptotic (local) flatness. After this, I will turn to instantons with toric symmetry. For an asymptotically locally Euclidean (ALE) or ALF gravitational instanton (M, g) with toric symmetry, the signature of (M, g) can be expressed directly in terms of its rod structure. Applying Hitchin?Thorpe-type inequalities for Ricci-flat ALE/ALF manifolds, one can formulate, as a step toward a classification of toric ALE/ALF instantons, necessary conditions that the rod structures of such spaces must satisfy. I will give a brief outline of these results, and then discuss the special case of rod structures with three turning points.

In diesem Vortrag tauchen wir ein in die überraschende Welt der Borwein-Integrale: scheinbar harmlose Integrale, deren Werte numerisch wie Pi aussehen - und sich doch manchmal um eine Winzigkeit von Pi unterscheiden.

Dieser Vortrag findet im Rahmen des Alumni-Tages 2025 der Universität Münster statt. Alle Interessierten sind herzlich willkommen.

Nach der Veranstaltung sind Sie in den Common Room des Exzellenzclusters "Mathematik Münster" zum Kaffee und weiteren Austausch eingeladen.

Wir bitten um Anmeldung: https://www.uni-muenster.de/Alumni/fuehrungenat.html

Abstract