Vorträge in der Woche 17.06.2019 bis 23.06.2019

Montag, 17.06.2019: Enumeration and properties of tree families

Prof. Dr. Stephan Wagner

I will review some classical results on the enumeration of different families of trees (such as binary trees, plane trees, and labelled trees) and discuss the distribution of various parameters of interest that can be associated with a tree. Typical examples are the number of leaves or the height of a tree.

Montag, 17.06.2019: The shape of tanglegrams

Prof. Dr. Stephan Wagner (Universität Stellenbosch)

A tanglegram consists of a pair of binary trees with the same number of leaves and a perfect matching between those leaves. The problem of enumerating tanglegrams (up to isomorphism) was recently solved by Billey, Konvalinka and Matsen. In this talk, we look at the shape of a randomly selected tanglegram - as it turns out, the two halves "essentially" look like two plane binary trees selected independently and uniformly at random.

Dienstag, 18.06.2019: Arithmetic Quantum Unique Ergodicity I

Claudius Kamp

Dienstag, 18.06.2019: Two Ways to Derive the Bogoliubov Time Evolution for Bose Gases in a Large Volume

Prof. Sören Petrat (Jacobs University Bremen)

We consider the dynamics of N bosons in a mean-field limit in large volume. It is well known that to leading order the N-body Schroedinger dynamics can be approximated by the Hartree equation. This talk is about the Bogoliubov approximation, which is the next-to-leading order correction that also describes the fluctuations around the mean-field Hartree state. I will present two ways of rigorously deriving this approximation in the setting where both the volume and the density of the gas tend to infinity and the interaction is scaled with the inverse density. This is joint work with Peter Pickl and Avy Soffer.

Freitag, 21.06.2019: Arithmetic Quantum Unique Ergodicity Ia

Claudius Kamp