Vorträge in der Woche 30.05.2022 bis 05.06.2022

Montag, 30.05.2022: Aufbau eines fachspezifischen Fragebogens und Online-Workshops zum Mindset nach Dweck

Jana Rehberg (Goethe-Universität Frankfurt)

Warum geben manche Personen nach Rückschlägen auf, während andere mit ähnlichen Voraussetzungen die nächste Herausforderung suchen? Dieser Frage geht die Mindset-Forschung, basierend auf den "theories of intelligences" nach Dweck, auf den Grund. Inzwischen konnte eine Vielzahl von Studien zeigen: der Glaube darüber, ob Intelligenz eine entwickel- oder unveränderbare Eigenschaft ist, kann einen Einfluss darauf haben, ob Menschen bereit sind, sich Herausforderungen zu stellen, aus Fehlern zu lernen und wie konstruktiv sie mit Rückschlägen umgehen. An dem einen Ende des Mindset-Spektrums glauben Menschen, dass Intelligenz und Talent vollständig angeboren und somit unveränderbar zu einer Person gehören (Fixed Mindset). Am anderen Ende des Spektrums glauben Menschen, dass diese Eigenschaften immer weiter entwickel- und ausbaubar sind (Growth Mindset). In der Regel positionieren sich Personen entlang dieses Spektrums und sind selten an den Extremen zu verorten. Zudem zeigt sich, dass das Mindset einer Person sowohl bereichs- als auch situationsspezifisch sein kann...

Mittwoch, 01.06.2022: Tropical homology over discretely valued fields

Dr. Matilde Manzaroli ( Universität Tübingen )

The talk is about a work in progress with Emiliano Ambrosi. Ilia Itenberg, Ludmil Katzarkov, Grigory Mikhalkin and Ilia Zharkov proved in “Tropical homology” that for a smooth proper family of complex varieties over the punctured disk with smooth tropicalisation X the Hodge numbers of the general fiber coincide with the dimensions of the tropical homology groups of X. We explore the possibility of extending this result over more general discrete valued fields of arithmetic interest, such as R((t)) or Qp, the field of p-adique numbers. In the process of doing this, we get an action of the Galois group on the tropical homology groups and we compare this action, in certain cases, with the action defined by Tyler Foster in “Galois actions on analytifications and tropicalisation”.

Donnerstag, 02.06.2022: Huisken-Yau-type uniqueness for area-constrained Willmore spheres

Prof. Dr. Jan Metzger (Universität Potsdam)

Let (M, g) be a Riemannian 3-manifold that is asymptotic to Schwarzschild. We study large area-constrained Willmore spheres $\Sigma\subset M$ with non-negative Hawking mass and inner radius $\rho$ dominated by the area radius $\lambda$. We show that if the scalar curvature of $(M,g)$ is non-negative, then there are no such surfaces with $\log\lambda \ll \rho$. The proof is based on a Ljapunov-Schmidt reduction for the (area constrained) Willmore functional and a detailed analysis of the reduced functional governing the position of such surfaces.

Donnerstag, 02.06.2022: Gorenstein 3-Fanos von Picardzahl 1 mit einer 2-Torus Wirkung

Andreas Bäuerle (Universität Tübingen)

Wir klassifizieren die dreidimensionalen, nichttorischen, Q-faktoriellen, log terminalen, Gorenstein Fano Varietäten von Picardzahl eins, die eine effektive Wirkung eines zweidimensionalen Torus besitzen.

Donnerstag, 02.06.2022: Stability of AVTD Behavior for Polarized T^2-Symmetric Space-Times

Prof. Dr. Jim Isenberg (University of Oregon, USA)

JoMaReC: One of the most effective tools for proving that Strong Cosmic Censorship holds for a family of cosmological solutions of Einstein’s equations is to verify that these solutions all exhibit Asymptotically Velocity Term Dominated (AVTD) behavior in a neighborhood of their Big Bang singularities. After presenting some background history of known results and conjectures concerning the behavior of the gravitational field near the Big Bang in cosmological solutions of Einstein’s equations, we discuss recent work with Ellery Ames, Florian Beyer, and Todd Oliynyk in which we prove that polarized T^2-Symmetric vacuum solutions in a neighborhood of Kasner solutions all exhibit AVTD behavior close to the initial singularity. We also discuss our very recent extension of these results to the case of non-vanishing cosmological constant.

Donnerstag, 02.06.2022: Topological insulators and dimensional reduction

Hannah Price (ETH Zürich)

Topological insulators are materials that, like a typical insulator, have a band gap in the bulk of the material. Unlike a typical insulator, topological insulators also have conducting states along the boundary that are topological protected, i.e. these states will remain conductive with arbitrary perturbations. The mechanisms underlying topological insulators are closely related to the mechanisms responsible for superconducting states, the quantum hall effect and the spin quantum hall state. By studying the symmetry of a material and perturbations under these symmetries, we can determine if a material has one of these topologically protected conductive states, and classify this type of protective state. We first look into symmetry classifications based on random matrix theory to find the Altband-Zirnbauer classification of symmetry classes. Additionally, we look into an alternative classification system based on the space of Dirac Hamiltonians, created by Bernard and Leclair. We can determine if a given class is a topological insulator in a given dimension by examining the topology of the given class. There are several approaches to determining the topological classification of a symmetry class. We will briefly discuss the use of homotopy groups, which is particularly useful in lower dimensions. Next, we will discuss the use of winding numbers and Chern numbers to classify these states, as well as the method of dimensional reduction to simplify the analysis. Finally, we analyze the hamiltonian of boundary to states in search of gapless states which imply a topological insulator in the bulk, and give an example of this technique for the 1D Dirac Hamiltonian.

Freitag, 03.06.2022: Rationale Homotopietheorie und (minimale) Sullivan-Modelle

Pascal Zeller (Universität Tübingen)