Vorträge

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.

Donnerstag, 13.11.2025: Volume preserving mean curvature flow in asymptotically flat spaces

Jacopo Tena (Rome)

In this talk, I will discuss relations between curvature flows and foliations of asymptotically flat manifolds. Firstly, I will extend to the asymptotically flat setting a classical result by Huisken-Yau which allows one to construct a constant mean curvature foliation of the outer part of the manifold by an alternative approach to those by Nerz and Eichmair-Koerber. This is a joint work with C. Sinestrari. Secondly, I will provide an alternative construction of the constant spacetime-mean curvature foliation of an initial data set by Cederbaum-Sakovich by introducing a (volume preserving) fully nonlinear mean curvature flow whose speed takes into account the non-time-symmetric nature of the ambient.

Donnerstag, 13.11.2025: TBA

Dr. Barbara Roos (L'Aquila)

Donnerstag, 13.11.2025: TBA

Dr. Harman Preet Singh (Tübingen)

Mittwoch, 26.11.2025: The 1-fold tropical Abel-Prym map

Giusi Capobianco (Roma Tor Vergata)

The algebraic Abel-Prym map relates the geometry of a double cover of algebraic curves with their corresponding Prym varieties. Birkenhake and Lange proved that the map has degree 2 if and only if the source curve is hyperelliptic. In the talk I will present joint work with Yoav Len, in which we investigate the 1-fold Abel-Prym map in the tropical setting and prove similar results. I will show that the tropical Abel-Prym map is a harmonic morphism of degree 2 if and only if the source graph is hyperelliptic. Furthermore, I will prove that the Jacobian of the image of this map is isomorphic, as pptav, to the Prym variety of the cover and relate this result to the tropical bigonal construction.

Montag, 12.01.2026: tba

Stefan Friedl