Vorträge in der Woche 29.05.2017 bis 04.06.2017

Montag, 29.05.2017: Non-archimedean and tropical geometry

Annette Werner (Frankfurt)

Vor-Kolloquium ab 16:00 Uhr: Berkovichräume und tropische Varietäten - eine Einführung. Zusammenfassung: This talk deals with the interplay between tropical varieties and non-archimedean analytic varieties in the sense of Berkovich. The Berkovich space associated to a variety over a field with a non-archimedean valuation contains a lot of points which are not visible in algebraic geometry. Under certain conditions these additional points are helpful to find tropical varieties inside Berkovich spaces. After an introduction explaining tropicalizations and Berkovich spaces, we will discuss some results from joint work with Joseph Rabinoff and Walter Gubler.

Dienstag, 30.05.2017: Deformation of metrics towards constant scalar curvature

Prof. Dr. Simon Brendle (Columbia University)

The classical uniformization theorem asserts that any Riemannian metric on a closed two- dimensional surface is conformal to a metric of constant Gaussian curvature. A higher dimensio- nal analogue of this statement is given by the solution of the Yamabe problem: Any metric on an n-dimensional manifold is conformal to a metric of constant scalar curvature. This problem is equivalent to the existence of a positive solution of the nonlinear elliptic equation of the form $\Delta u - \frac{n-2}{4(n-1)} R u + c u^{\frac{n+2}{n-2}} = 0$. In this lectures, I will describe the background of this problem, and its variational formulation in terms of the Yamabe functional. The gradient flow associated with the Yamabe functional leads to an curvature flow, and I will discuss why this flow converges to a metric of constant scalar curvature for any initial metric.

Dienstag, 30.05.2017: Cuspidal representations

Polyxeni Spilioti