22.11.2022

Stephan Stadler (MPIM Bonn)

Title

Periodic CAT(0) spaces

Abstract

A guiding principle in CAT(0) geometry is that in the presence of enough symmetry failure of hyperbolic behaviour can be attributed to flat pieces -- isometric embeddings of unbounded higher dimensional  Euclidean regions. For instance, an axial isometry acts with north-south dynamics unless one (and then every) axis  bounds a flat half-plane. In the smooth setting, the structure theory of Ballmann et al. implies the following striking result. If a discrete group G acts on a Hadamard manifold H with finite volume quotient, and every G-axis bounds a flat half-plane,  then H has to be isometric to a symmetric space or split as a metric product. Motivated by this and the general tendency in non-positive curvature that much of the smooth theory generalizes to the synthetic setting, Ballmann and Buyalo formulated two conjectures which predict a dichotomy in the geometric behaviour of periodic CAT(0) spaces according the appearing amount of flatness. In the talk I will discuss these conjectures, I will survey what is
known and report on recent progress.

Schedule

10:00 - 11:30 RTG Lecture 1 (Ana Chavez-Caliz)  | INF 230/231, COS, EG, SR 00.001 (kleiner Hörsaal von 10.00 - 12.00)
11:30 - 12:00 Get-Together with speaker | INF 230/231, COS, EG, SR 00.001
12:00 - 13:00 Common lunch | reserved at BräuStadel
13:00 - 13:30 Informal meeting of PhD Students | INF 205, Mathematikon, SR B
13:30 - 14:30 RTG Colloquium: Stephan Stadler | INF 205, Mathematikon, SR B
14:30 - 15:15 Common coffee/ tea | INF 205, Mathematikon, Foyer UG
15:15 - 16:45 RTG Lecture 2  (Ana Chavez-Caliz)  | INF 230/231, COS, EG, SR 00.001 (kleiner Hörsaal von 15.00 - 17.00)

HD