401-3533-DRL  Generalized Nonpositive Curvature

SemesterAutumn Semester 2022
LecturersU. Lang
Periodicitynon-recurring course
Language of instructionEnglish
CommentOnly for ZGSM (ETH D-MATH and UZH I-MATH) doctoral students. The latter need to register at myStudies and then send an email to Link with their name, course number and student ID. Please see Link


AbstractCAT(0) spaces, Busemann convex spaces, metric spaces with convex geodesic bicombings; injective metric spaces and injective hulls; Gromov hyperbolicity, Helly graphs and Helly groups; fixed points, barycenter constructions, and applications.
Objective
Lecture notesLectures notes will be provided.
Literature- M. R. Bridson, A. Haefliger: Metric Spaces of Non-Positive Curvature, Springer 1999
- A. Papadopoulos: Metric Spaces, Convexity and Nonpositive Curvature, EMS 2005
- U. Lang: Injective hulls of certain discrete metric spaces and groups, J. Topol. Anal. 5 (2013), 297-331
- D. Descombes, U. Lang: Convex geodesic bicombings and hyperbolicity, Geom. Dedicata 177 (2015), 367-384
- J. Chalopin et al.: Weakly Modular Graphs and Nonpositive Curvature, Memoirs AMS 268 (2020), no. 1309
- J. Chalopin et al.: Helly groups, arXiv:2002.06895v2 [math.GR]
Prerequisites / NoticeBasic knowledge of Riemannian geometry and functional analysis will be assumed.
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
Techniques and Technologiesassessed
Method-specific CompetenciesAnalytical Competenciesassessed
Problem-solvingassessed
Personal CompetenciesCreative Thinkingassessed
Critical Thinkingassessed