CAT(0) Cube Complexes

CAT(0) Cube Complexes

Semester
SoSe 2023

Lecturer
Clara Löh, Kevin Li, Matthias Uschold

Type of course (Veranstaltungsart)
Seminar

German title
CAT(0)-Würfelkomplexe

Contents
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.

Recommended previous knowledge
basic group theory, basic theory of metric spaces

Time/Date
Mi 8:30--10:00

Location
M 102

Course homepage
https://loeh.app.ur.de/teaching/cccsem_ss23
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Organisational meeting/distribution of topics: Thu, Feb 9, 12:00 (s.t.), M 101; if you cannot
attend the organisational meeting, please send an email to one of the organisers
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Presentation: Giving a seminar talk of roughly 90 minutes

Examination (Prüfungsleistungen)

Detailed written report of the seminar talk

Modules
BSem, MV, MSem, LA-GySem

ECTS
BSem, MV, MSem: 4,5 ECTS. LA-GySem: 6 ECTS

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