Vorträge in der Woche 14.05.2018 bis 20.05.2018

Montag, 14.05.2018: Bose-Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature

Dr. Andreas Deuchert (IST Austria)

Dienstag, 15.05.2018: Zufällig punktierte simpliziale Komplexe und Benjamini-Schramm Konvergenz von Bettizahlen

Michael Schroedl (KIT Karlsruhe)

Man erhält ein Maß auf dem Raum der punktierten simplizialen Komplexe, in dem man in einem endlichen simplizialen Komplex zufällig eine Ecke wählt. Diese Maße erfüllen die Eigenschaft der Unimodularität, welche sich auch für unendliche simpliziale Komplexe definieren lässt. Für diese Klasse von Maßen werde ich eine Definition von Bettizahlen geben. Außerdem werde ich den Begriff der Benjamini-Schramm Konvergenz einführen, was eine Form der „lokale Konvergenz“ ist und zeigen wie sich die Bettizahlen unter dieser verhalten.

Donnerstag, 17.05.2018: Geometric flows and singularity formation

Prof. Dr. Simon Brendle (Columbia University)

In these lectures, I will discuss the formation of singularities for embedded, mean convex hypersurfaces evolving under mean curvature flow. Among other things, I will discuss the main a-priori estimates, and some recent results on the classification of singularity models. For example, for two-dimensional surfaces in R^3 (or for uniformly two-convex hypersurfaces in higher dimensions), the only possible singularity models are the shrinking spheres, shrinking cylinders, and the rotationally symmetric bowl soliton.

Donnerstag, 17.05.2018: Wave-packet dynamics in locally periodic media

Dr. Alexander Watson (Duke University)

We study the dynamics of wave-packet solutions of Schr\”{o}dinger’s equation and Maxwell’s equations in media with a local periodic structure which varies adiabatically (over many periods of the periodic lattice) across the medium. We focus in particular on the case where symmetries of the periodic structure lead to degeneracies in the Bloch band dispersion surface. We systematically and rigorously derive the `anomalous velocity’ of wave-packets due to the Bloch band’s Berry curvature, and the dynamics of a wave-packet incident on a Bloch band degeneracy in one spatial dimension. Joint work with Michael Weinstein and Jianfeng Lu.

Donnerstag, 17.05.2018: On the Average-Field Functional for Anyons

Dr. Michele Correggi (Sapienza University, Rom, Italy)

We discuss the average-field approximation for a trapped gas of non-interacting anyons in the quasi-bosonic regime. In the homogeneous case, i.e., for a confinement to a bounded region, we prove that the energy in the regime of large statistics parameter, i.e., for "less-bosonic" anyons, is independent of boundary conditions and of the shape of the domain. When a non-trivial trapping potential is present, we derive a local density approximation in terms of a Thomas-Fermi-like model. We also discuss some recent numerical simulations and certain open questions mostly related to the vortex structure of the minimizer. Joint work with R. Duboscq (Toulouse), D. Lundholm (Stockholm) and N. Rougerie (Grenoble).