Vorträge in der Woche 01.11.2021 bis 07.11.2021

Dienstag, 02.11.2021: Struktur normkompakter Operatorhalbgruppen

P. Hermle (Wuppertal)

Kompakte Operatorhalbgruppen spielen eine wichtige Rolle in der asymptotischen Analyse dynamischer Systeme. Ein zentrales Strukturresultat über schwach bzw. stark kompakte Operatorhalbgruppen ist das Theorem von Jacobs-de Leeuw-Glicksberg. Im Vortrag verfeinern wir dieses Theorem für Operatorhalbgruppen, welche bezüglich der Normtopologie kompakt sind. Außerdem diskutieren wir, welche Voraussetzungen ein Operator auf einem Banachraum erfüllen muss, sodass die von ihm erzeugte monothetische Operatorhalbgruppe kompakt. Dieser Vortrag findet im Rahmen der Veranstaltung "Operator Theoretic Aspects of Ergodic Theory" statt. Näheres dazu findet man unter https://ergodic.de

Dienstag, 02.11.2021: Y-pieces

Anton Deitmar

Donnerstag, 04.11.2021: Tropical Enumerative Invariants on Toric surfaces

Parisa Ebrahimian (University of Tehran)

In this talk, I will first introduce 4 tropical enumerative problems which all are about counting the number of plane curves on P^2, F_0, and F_2 satisfying incidence conditions. Then I will talk about the ambient spaces that are toric surfaces and the tropical curves on them with more details so as to clarify the problems. In the end, Kontsevich's formula and its generalizations which are the solutions to our enumerative problems will be introduced. Then if I have time, I will talk about the main step of the proof of these formulas by using tropical intersection theory.

Donnerstag, 04.11.2021: Singularity theorems in low regularity

Dr. Melanie Graf (Universität Tübingen)

JoMaReC: The singularity theorems of R. Penrose and S. Hawking from the 1960s show that a spacetime satisfying certain physically reasonable curvature and causality conditions cannot be causal geodesically complete. Despite their great success these classical theorems still have some drawbacks, one of them being that they require smoothness of the metric while in many physical models the metric is less regular. In my talk I will present work on singularity theorems based on distributional energy conditions for metrics that are merely continuously differentiable – a regularity where one still has existence but not uniqueness for solutions of the geodesic equation. We will see that an approximation-based approach to the low-regularity issue is closely linked to establishing singularity theorems under weakened energy conditions and while the improvements necessary are still entirely straightforward in the present case, attempting to lower the regularity further would require some new methods.

Donnerstag, 04.11.2021: Thermalization in Kitaev’s quantum double models

Angelo Lucia (Universidad Complutense de Madrid)

Is it possible to have a 2D self-correcting memory? The general belief that this is not the case usually lies upon the absence of a strong enough energy barrier preventing errors and noise to quickly destroy the information encoded in the memory. But this is not sufficient, as there are entropic factors at play that could take the role of the energy barrier, by delaying the spread of errors. In order to really settle the question, one should look directly at the time required for the memory to thermalize. In this talk, I will consider Kitaev's Quantum Double models with arbitrary group (including the non-abelian case). I will present a recent work in which, using tensor network techniques, we are able to prove that the thermalization dynamic given by Davies' generators has a spectral gap, therefore excluding the possibility of self-correction for this class of models. Based on joint work with David Pérez-García and Antonio Pérez-Hernández. arxiv:2107.01628