Vorträge in der Woche 27.01.2025 bis 02.02.2025

Montag, 27.01.2025: Vortrag in der Reihe "Mathematiker:innen im Beruf" - Risikomanagement in lokalen Stadtwerken

Dr. Oliver Schön (Stadtwerke)

In der Vortragsreihe "Mathematiker:innen im Beruf", die sich vor allem an die Studierenden des Fachbereichs Mathematik richtet, berichten Mathematiker über ihren Werdegang, ihr jetziges Arbeitsfeld und wie ihnen ihr Mathematikstudium dabei zu gute kommt. --- Zum Vortrag: Die Energiebeschaffung steht vor großen Herausforderungen: Volatile Märkte, unvorhersehbare Nachfrage, erneuerbare Energien und politische Einflüsse. Hier kommen mathematische Modelle ins Spiel. Als Mathematiker im Risikomanagement eines lokalen Stadtwerks beschäftige ich mich täglich mit der Analyse und Steuerung dieser Risiken. In meinem Vortrag gebe ich Einblicke, wie mathematische Methoden – von stochastischen Prozessen bis zur Optimierung – dazu beitragen, Beschaffungsstrategien zu entwickeln, die sowohl wirtschaftlich effizient als auch sicher für die Energieversorgung sind. Ich zeige, wie Theorie und Praxis zusammenwirken und warum Mathematiker an dieser Stelle unterstützen können.

Donnerstag, 30.01.2025: Singularity Theories of Matter, Weak Second Bianchi Identity, and Bray's Mass of ZASS

Prof. Dr. A. Shadi Tahvildar-Zadeh (Rutgers University)

The second Bianchi identity is a differential curvature identity that is satisfied on any manifold with a smooth metric. If the metric of a Lorentzian manifold solves the Einstein equations, the twice contracted version of the second Bianchi identity implies the physical laws of energy and momentum conservation for the matter field permeating the spacetime. In this talk I define a distributional version of the twice-contracted second Bianchi identity, and show that it holds for spacetimes with time-like curvature singularities, provided that these singularities are in a precise sense not too strong. The momentum and energy balance laws that follow from this assertion could potentially be used to develop a theory, first envisioned by Weyl, in which worldlines of matter particles are identified with time-like singularities of an otherwise vacuum spacetime. As a first application, a large class of spherically symmetric static Lorentzian metrics with time-like one-dimensional singularities is identified, for which the identity holds. The proof uses the machinery of zero-area singularities (ZASS) and the notion of mass for them as defined by H. Bray. This is joint work with A. Burtscher and M. Kiessling.

Donnerstag, 30.01.2025: Macroscopic Thermalization for Highly Degenerate Hamiltonians

Cornelia Vogel (Tübingen)

An isolated macroscopic quantum system thermalizes if its initial state eventually reaches a suitable thermal equilibrium subspace and stays there for most of the time. For non-degenerate Hamiltonians, a sufficient condition for the thermalization of every initial state is an appropriate version of the eigenstate thermalization hypothesis (ETH). Shiraishi and Tasaki recently proved the ETH for a perturbation of the Hamiltonian of a large number of free fermions on a one-dimensional lattice. The perturbation is needed to remove the high degeneracies of the Hamiltonian. We point out that also for degenerate Hamlitonians, all initial states thermalize if the ETH holds for every eigenbasis, and we show that this is the case for free fermions in 1d. Additionally, we develop another strategy of proving thermalization by adding small generic perturbations to Hamiltonians for which it can be shown that one eigenbasis (but not necessarily all) fufills the ETH. This strategy applies to arbitrarily small generic perturbations of the Hamiltonian of free fermions in arbitrary spatial dimensions. This is joint work with Barbara Roos, Stefan Teufel and Roderich Tumulka.

Freitag, 31.01.2025: TBA

Danko Moisés Aldunate Bascunán (Universidad Católica de Chile)