Vorträge in der Woche 27.01.2025 bis 02.02.2025
Vorherige Woche Nächste Woche Alle Vorträge
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.
Uhrzeit: | 16:00 - 16:45 |
Ort: | N14 + Zoom: https://zoom.us/j/97549530110 |
Gruppe: | Kolloquium |
Einladender: | Fachschaft Mathematik + Studiendekan |
Dienstag, 28.01.2025: Weak injectivity radius property and spectral geometry 2
Daniel Funck
Uhrzeit: | 14:15 |
Ort: | C9A03 |
Gruppe: | Oberseminar Analysis un Zahlentheorie |
Einladender: | Deitmar |
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.
Uhrzeit: | 14:00 |
Ort: | Seminarraum S09 (C6H05) and virtual via zoom, for zoom link please contact Martina Neu |
Gruppe: | Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
Einladender: | Carla Cederbaum, Gerhard Huisken, zusammen mit Jan Metzger (Potsdam) |
Donnerstag, 30.01.2025: Spectral Stability in one dimensional nonlinear Dirac equation with Soler-type nonlinearity
Danko Moisés Aldunate Bascunán (Universidad Católica de Chile)
We establish for the 1D Soler model with power nonlinearities $f(s)=s|s|^{p-1}$, $p>0$, that the upper-right block operator~$L_0$ of the linearized operator satisfies: its ground states $-2\omega$ and $0$ are its only two eigenvalues in the gap of its essential spectrum if only if $p\geq1$. Our second main result is the simplicity of generalized eigenfunction at the threshold of the essential spectrum for Dirac operators with potential. These results apply in particular to lower-left block operator~$L_\mu$.
Uhrzeit: | 14:15 |
Ort: | online - wenn Sie Zugang haben wollen, schicken Sie bitte eine Nachricht an Elena Kabagema-Bilan |
Gruppe: | Oberseminar Mathematical Physics |
Einladender: | Keppeler, Lemm, Pickl, Teufel, Tumulka |
Donnerstag, 30.01.2025: Variational wave packets for magnetic Schrödinger equations: observable error analysis and time-integration
Caroline Lasser (TU München)
We consider the magnetic Schrödinger equation in semiclassical scaling, which describes the dynamics of particles under the influence of a magnetic field. The solution is approximated by a single Gaussian wave packet via the time-dependent Dirac-Frenkel principle. We discuss observable error estimates and time-integration of the parameter evolution by a version of the Boris algorithm for classical charged particle dynamics. This is joint work with Kurt Busch, Marlis Hochbruck, and Malik Scheifinger.
Uhrzeit: | 14:15 |
Ort: | C2A17 |
Gruppe: | Numerische Mathematik |
Einladender: | Lubich |
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.
Uhrzeit: | 15:15 |
Ort: | C4H33 |
Gruppe: | Oberseminar Mathematical Physics |
Einladender: | Keppeler, Lemm, Pickl, Teufel, Tumulka |
Donnerstag, 30.01.2025: Large scale response of gapless 1d and quasi-1d fermionic systems
Harman Preet Singh (SISSA, Italien)
For a class of non-interacting, one-dimensional gapless system of lattice fermions, we consider the density and current dynamical responses to a time-adiabatic density-type perturbation, in the infinite volume and zero temperature limit. Furthermore, we consider the edge density and current responses for quantum Hall lattice systems on a cylinder. We prove the validity of the linear response for such quantities, thus justifying Kubo’s formula. Further, we explicitly evaluate them solely in terms of spectral data at the Fermi points, and of the profile of the perturbation. The proof of validity of linear response on the physically relevant time-scale relies on a precise analysis of the imaginary-time Duhamel series, and in particular on a cancellation for the scaling limit of the higher order correlation functions describing the nonlinear response, also related to bosonization. The precise form of the linear response coefficient is then fixed by lattice conservation laws. Finally, I will discuss how to generalise such results to the case of weakly interacting fermions, an ongoing joint project with M. Porta and G. Scola. The talk will be based on arXiv:2411.04023, a joint work with Marcello Porta.
Uhrzeit: | 16:30 |
Ort: | C3N14 |
Gruppe: | Oberseminar Mathematical Physics |
Einladender: | Keppeler, Lemm, Pickl, Teufel, Tumulka |