Kolloquien SS 2019

Freitag, 03.05.2019: Exponentielle Integratoren

Marlis Hochbruck (KIT)

Freitag, 03.05.2019: Über hochdimensionale und noch höherdimensionale Gleichungen

Harry Yserentant (TU Berlin)

Montag, 06.05.2019: Arithmetic and geometry of algebraic surfaces: the place of elliptic fibrations and K3 surfaces

Cecilia Salgado (Universidade Federal do Rio de Janeiro)

In this talk I will go over recent progress on the arithmetic of algebraic surfaces, review some contributions of the study of elliptic fibrations to it and present open problems summarizing the state of the art. K3 surfaces have a special place in the classification of algebraic surfaces: they lie in an intermediate spot, being not too simple (as rational surfaces) nor too complicated (as surfaces of general type). They are ubiquitous in mathematics, having been studied by differential and algebraic geometers, dynamicists, arithmeticians, analysts and also by physicists. A special feature of K3 surfaces is that they are the only class of surfaces that might admit more than one elliptic fibration, with section, that is not of product type. The classification of such different fibrations has been the object of several papers since the 90's. I plan to outline a new approach to this problem and, if time allows, discuss arithmetic and geometric applications of the method.

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.