Uniformization of dynamical systems and diophantine problems
Friday, 8.11.19, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
This is joint work with Gareth Boxall (Stellebosch University) and Gareth Jones (University of Manchester). We investigate certain number theoretic properties of polynomial dynamical systems, using the notion of a uniformization at infinity. In this talk I will explain how the ideas involved can be used in order to tackle various related problems\n on diophantine geometry.\n
Automorphisms of foliations
Friday, 22.11.19, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
We will discuss in various contexts the transverse finiteness of the group of automorphisms/birational transformations preserving a holomorphic foliation. This study provides interesting consequences for the distribution of entire curves on manifolds equipped with foliations and suggest some generalizations of Lang’s exceptional loci to non-special manifolds, in the analytic or arithmetic setting. \nThis is a work in progress with F. Lo Bianco, J.V. Pereira and F. Touzet.
Klein's Quartic, Fermat's Cubic and Rigid Complex Manifolds of Kodaira Dimension One
Friday, 29.11.19, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
The only rigid curve is \(\bmathbb P^1\). Rigid surfaces exist in Kodaira dimension \(-\binfty\) and \(2\).\nIngrid Bauer and Fabrizio Catanese proved that for each \(n \bgeq 3\) and for each \(\bkappa = -\binfty, 0, 2,\bldots, n\) there is a rigid \(n\)-dimensional projective manifold with Kodaira dimension \(\bkappa\). In this talk we show that the result also holds in Kodaira dimension one.\n\n