Vorträge in der Woche 29.11.2021 bis 05.12.2021

Dienstag, 30.11.2021: Stability of timelike minimal surfaces in expanding spacetimes

Philip Thonke (Universität Potsdam)

The timelike minimal surface equation is a degenerate hyperbolic system describing the motion of a relativistic membrane, or p-brane. Using a harmonic map gauge, Olaf Milbredt has obtained local well-posedness results for the corresponding Cauchy-Problem under suitable geometric assumptions. Much less is known, however, about global well-posedness and stability of a solution with respect to small-data perturbations when the spacetime is not Minkowski-Space. In this talk I shall give an introduction to the theory aswell as a short overview of the existing literature and then present some stability results for the case of a membrane moving in an expanding spacetime that is not necessarily spatially homogenuous.

Dienstag, 30.11.2021: Teichmüller space

Jan Feldmann

Donnerstag, 02.12.2021: Realizability of tropical pluri-canonical divisors

Felix Roehrle ( Universität Frankfurt )

A tropical curve is a vertex-weighted metric graph. A tropical pluri-canonical divisor is a divisor linearly equivalent to an integer multiple of the tropical canonical divisor. In this talk I will present a criterion to decide whether a given instance of this tropical data is the tropicalization of a smooth algebraic curve with a $k$-differential. To do so, I will present a result by Bainbridge-Chen-Gendron-Grushevsky-Möller that identifies degenerations of smooth curves with $k$-differentials as so-called twisted $k$-differentials. I will then show that tropical curves with pluri-canonical divisors have the same underlying combinatorics as twisted $k$-differentials. This reduces the initial realizability problem to a lifting problem for tropical data to twisted $k$-differentials. I will present the various local and global obstructions to this and develop a language which allows to state the main theorem. This is joint work with Johannes Schwab.

Donnerstag, 02.12.2021: Situationales Interesse von Schülerinnen und Schülern beim Bearbeiten physikalischer Lernaufgaben in biologischen und technischen Kontexten

Johannes Lewing (Universität Göttingen)

Zur Förderung des Interesses und zur Verringerung interessenbezogener Genderdifferenzen geraten im naturwissenschaftlichen Unterricht vermehrt kontextorientierte und fächerübergreifende Unterrichtsansätze in den Vordergrund. Während der positive Einfluss der Kontextorientierung gegenüber traditionellen Unterrichtsansätzen auf das Interesse empirisch gut belegt ist, stellt sich die Frage, wie unterschiedliche Kontexte wirken. Aus diesem Grund wird in der vorliegenden Studie die systematische Variation des Kontexts von Lernaufgaben und der Einfluss auf das situationale Interesse bei der Bearbeitung untersucht. Dazu wurden isomorphe Lernumgebungen in biologischen und technischen Kontexten entwickelt, welche von Schülerinnen und Schülern der 10. Jahrgangsstufe bearbeitet wurden. Für die Aufgaben wurde das Energiekonzept aufgrund seiner zentralen Stellung in den Naturwissenschaften und seiner Interdisziplinarität als Lerngegenstand gewählt. Die Studie wurde von N = 315 Schülerinnen und Schülern in Form einer Online-Lernumgebung durchgeführt. Im Beitrag werden die Ergebnisse der Studie vorgestellt und Implikationen für die Schulpraxis diskutiert.

Donnerstag, 02.12.2021: From Normalizable to Non-Normalizable Measures: a Survey through the Boltzmannian Paradigm

Cedric Igelspacher (Tübingen)

The talk adresses two conflicts: First, why is there irreversible macroscopic behavior in nature that is grounded in the microscopic dynamics being reversible. To answer this we will first go through the statistical account of Boltzmann clearing up this conflict between time-symmetric and time-asymmetric behavior as being typical. Low-entropy states evolve towards high-entropy states. After that we try to see how in the same setting the origin of low-entropy states can be explained by discussing the Boltzmann fluctuation scenario as well as the Past Hypothesis. The problems that arise through these leads us to a proposal made by Carroll and Chen which allows us to establish an arrow of time as a typical feature of our universe. However by doing this, we have to assume that the entropy can grow unbounded, hence the microcanonical measure becomes non-normalizable. Second, reasoning in Boltzmann’s way given the macrostate now, we should expect entropy to grow in both time directions. This seems uncompatible within a model that assumes entropy to be unbounded. We will see how this conflict can be resolved. After that we look at different kinds of reasoning that mainly rely on the fact that only a theory with unbounded entropy can give solid epistemic ground that is in accordance with us being ordinary observers and not boltzmann brains.

Donnerstag, 02.12.2021: The characteristic gluing problem of general relativity

Dr. Stefan Czimek (ICERM, Brown University, USA)

JoMaReC: In this talk we introduce and solve the characteristic gluing problem for the Einstein vacuum equations. We prove that obstructions to characteristic gluing come from an infinite-dimensional space of conservation laws along null hypersurfaces for the linearized equations at Minkowski. We show that this obstruction space splits into an infinite-dimensional space of gauge-dependent charges and a 10-dimensional space of gauge-invariant charges. We identify the 10 gauge-invariant charges to be related to the energy, linear momentum, angular momentum and center-of-mass of the spacetime. Based on this identification, we explain how to characteristically glue a given spacetime to a suitably chosen Kerr black hole spacetime. As corollary we get an alternative proof of the Corvino-Schoen spacelike gluing to Kerr. Moreover, we apply our characteristic gluing method to localise characteristic initial data along null hypersurfaces. In particular, this yields a new proof of the Carlotto-Schoen spacelike localization where our method yields no loss of decay, thus resolving an open problem in this direction. We also outline further applications. This is joint work with S. Aretakis (Toronto) and I. Rodnianski (Princeton).

Donnerstag, 02.12.2021: (Symmetry protected) topological phases in open systems

Caroline de Groot (MPQ München)

We address the question of whether symmetry protected topological order (SPTO) exists in open systems by preserving both equivalence classes and order parameters. To this end we consider which symmetric channels map within a manifold of SPT mixed states. The first important result is proving that a strong symmetry (SS) condition on channels maps a one-dimensional SPT phase to itself and equivalently maps a string order parameter's pattern of zeros back to the same pattern of zeros at finite time. This is a sufficient condition for preserving the notion of a cocycle. This allows us to define an equivalence class of SPT mixed states through fast dissipative Lindbladian evolution (Coser and Perez-Garcia, 2019). We crucially show that a notion of weak symmetry (WS) is too coarse-grained to preserve SPTO, which is evident in the string order parameter that is destroyed instantly with any finite decay. Asking which conditions transform between *different* SPTO leads to our second main result. Now requiring also *necessity of preservation of the cocycle* leads us to introduce twisted SS conditions which induce endomorphisms on the SPT phase and map SPT mixed states to SPT mixed states in a different phase.