Seminar: CAT(0) Cube Complexes; SS 2023

Prof. Dr. Clara Löh / Kevin Li / Matthias Uschold

News

There are still free slots! If you are interested in participating: please send an email to one of the organisers.
The templates for reports/handouts are online (see below); of course, you can also produce the report/handout by other means.
The organisational meeting for this seminar was on Thursday, February 9, at 12:00 (s.t.) in M 101.
Registration: through the GRIPS registration form (before 13.02.2023, 10:00).
The schedule is now available.
This seminar will be held in English. The written report can be in English or German. The handouts should be in English.

Seminar: CAT(0) Cube Complexes

In comparison geometry, geodesic triangles are compared with comparison triangles in a model geometry. In particular, in CAT(0)-geometry, geodesic triangles are "thinner" than in flat Euclidean space. This provides a direct metric approach to geometry of non-positive curvature.

Combining CAT(0)-geometry with combinatorial structure (such as cube complexes or median graphs) leads to a rich interaction between metric geometry, combinatorics, and geometric group theory.

In this seminar, we will learn the basic language of CAT(0)-complexes and median graphs and then study applications to topology, geometry, and group theory.

Several talks will also be suitable for students in the Lehramt Gymnasium track.

Time/Location

Wednesday, 8:30--10:00, M 102

Material

Overview of all talks.
Admin and preparation
Templates for the reports/handouts will be provided later.
LaTeX template for handouts: .tex, .pdf
LaTeX template for reports: .tex, .pdf

Additional material:

Hints on writing mathematical texts (in German)
More such hints
Small print on slide talks

Prerequisites

Basic group theory, basic theory of metric spaces

This seminar is suitable for Bachelor/Master students with an interest in groups and geometry; several talks will also be suitable for students in the Lehramt Gymnasium track. This seminar could be the starting point for a project under my supervision (e.g., bachelor/master thesis, Zulassungsarbeit).

Formalities/Credits

See the commented list of courses.

Last Change: April 14, 2023.