Vorträge in der Woche 03.11.2025 bis 09.11.2025

Dienstag, 04.11.2025: Direct integrals of sheaves

Giacomo Gavelli

Mittwoch, 05.11.2025: Hamiltonicity of simplicial hyperplane arrangements

Veronika Körber (Tübingen)

Central hyperplane arrangements are finite sets of hyperplanes in R^n that intersect only in 0. They are called simplicial, if every connected component of the complement is adjacent to precisely n hyperplanes. A tope graph of a central hyperplane arrangement is given by a set of vertices, one vertex per connected component of the complement, and a set of edges; two vertices are connected if their corresponding connected components are adjacent in the hyperplane arrangement. There is a conjecture stating that the tope graphs of central simplicial arrangements have a Hamiltonian cycle. We proved the Hamiltonicity for certain families of them.

Donnerstag, 06.11.2025: The Conformal Method and Hamiltonian General Relativity

David Maxwell (Fairbanks, Alaska)

The conformal method is a workhorse tool for building solutions of the Einstein constraint equations, especially those with constant mean curvature. One frequent perspective on the technique is that it is simply a handy tool, a frequently effective mathematical artifice. In this talk we demonstrate instead that the conformal method is deeply rooted in the Hamiltonian approach to general relativity. We start with a careful analysis of the Gauss constraint $\mathrm{div} E = \rho$ of electromagnetism and describe an approach, grounded in Hamiltonian field theory, for generating its solutions. Then, after an unexpected detour into temporal wave gauge in general relativity, we exhibit a modern understanding of conformal method as an immediate generalization of the toy-model approach to the Gauss constraint. If time permits, we discuss how these ideas led to recent advances in formulating the conformal method in the non-vacuum setting, with applications to charged fluids.