November 22nd, 2022

Date:
22.11.2022

Speaker:
Stephan Stadler (MPIM Bonn)

Title
Periodic CAT(0) spaces
AbstractA 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 northsouth dynamics unless one (and then every) axis bounds a flat halfplane. 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 Gaxis bounds a flat halfplane, then H has to be isometric to a symmetric space or split as a metric product. Motivated by this and the general tendency in nonpositive 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 ChavezCaliz)  INF 230/231, COS, EG, SR 00.001 (kleiner Hörsaal von 10.00  12.00)
11:30  12:00 GetTogether 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 ChavezCaliz)  INF 230/231, COS, EG, SR 00.001 (kleiner Hörsaal von 15.00  17.00)

Place:
HD