Oberseminare und sonstige Vorträge

A hypersurface of a Lorentzian manifold is called null, if its induced metric is degenerate. In such geometries, classical some geometric concepts are unavailable and for this reason there is little knowledge about curvature flows in such spaces. Building upon a definition of mean curvature flow I developed with Henri Roesch few years ago, we extend and improve the analysis to constrained mean curvature flows, which will then enable us to foliate large classes of null hypersurfaces by surfaces of constant spacetime mean curvature. This is joint work with Wilhelm Klingenberg (Durham) and Ben Lambert (Leeds).

A hypersurface of a Lorentzian manifold is called null, if its induced metric is degenerate. In such geometries, classical some geometric concepts are unavailable and for this reason there is little knowledge about curvature flows in such spaces. Building upon a definition of mean curvature flow I developed with Henri Roesch few years ago, we extend and improve the analysis to constrained mean curvature flows, which will then enable us to foliate large classes of null hypersurfaces by surfaces of constant spacetime mean curvature. This is joint work with Wilhelm Klingenberg (Durham) and Ben Lambert (Leeds).

The question of the existence of free subgroups in a given group traces back to a problem posed by von Neumann. When such subgroups exist, their genericity has been the focus of extensive research. In this talk, we formulate and investigate a version of the genericity question for subgroups of the affine group over a field of characteristic zero. Let $G$ denote the affine group over a field $F$, and let $\mu$ be a probability measure on $G \times G$. Consider the left or right random walk $(X_n, Y_n)$ on $G \times G$ driven by $\mu$. I will discuss several results on conditions under which the semigroup generated b $X_n$, $Y_n$ is free, either eventually or infinitely often. The talk is based on a work in progress with Richard Aoun.

TBA