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RTG Lecture “Asymptotic Invariants and Limits of Groups and Spaces” (Summer Semester 2018)

Lecture: Tuesday 9:45-13:00 SR 2.58
Tuesday 15:00-16:30 SR 1.067
Lecturer Prof. Dr. Roman Sauer
Office hours: by appointment
Room 1.001 Kollegiengebäude Mathematik (20.30)
Email: roman.sauer@kit.edu
Lecturer Prof. Dr. Wilderich Tuschmann
Office hours: by appointment
Room 1.002 Kollegiengebäude Mathematik (20.30)
Email: tuschmann@kit.edu

This semester’s RTG lecture will be split between courses by Wilderich Tuschmann on “Geometric Convergence and Finiteness Theorems and their Applications” and by Gye-Seon Lee on “Coxeter Groups and Geometry”.

Geometric Convergence and Finiteness Theorems and their Applications (Wilderich Tuschmann)

Abstract: I will discuss finiteness and infiniteness results for Riemannian manifolds with curvature bounds and, more generally, for Alexandrov spaces, along with applications inside and outside Riemannian geometry. The underlying concepts and techniques involve, among others, tools form comparison geometry, Cheeger-Gromov convergence of Riemannian manifolds, Gromov-Hausdorff convergence of metric spaces, and Cheeger-Fukaya-Gromov collapsing theory, and I shall also include primers on these topics as well.

Prerequisites: Some solid knowledge of differential geometry and algebraic and differential topology.

Coxeter Groups and Geometry (Gye-Seon Lee)

Abstract: Coxeter groups are finitely generated groups that resemble the groups generated by reflections. They play important roles in the various areas of mathematics. In particular there are many connections between Coxeter groups and geometry. This lecture focuses on how one can use Coxeter groups to construct interesting examples in geometry. It also provides a gentle introduction to the deformation theory of geometric structures along the way.