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DTSTART;VALUE=DATE:20230523T171500
DTEND;VALUE=DATE:20230523T171500
UID:13635@agenda.unifr.ch
DESCRIPTION:CAT(0) spaces originated from Riemannian geometry in the 50s as synthetic generalizations of Hadamard manifolds --\nsimply connected Riemannian manifolds of non-positive sectional curvature.\nAlready Riemannian geometry provides very interesting examples, like symmetric spaces of non-compact type. However,\nthe actual universe of CAT(0) spaces is much larger. While it contains many nice non-smooth examples which\ncarry additional combinatorial structures, like\ntriangulations or cubulations, mostly  coming from group theory, a general CAT(0) space is simply badly singular.\nGiven this wild zoo of spaces, one inevitably seeks a form of classification.\nA CAT(0) space is said to have higher rank if every geodesic lies in a flat plane.\nOtherwise it is said to have rank 1.\nBallmann's Rank Rigidity Conjecture classifies CAT(0) spaces X with a cocompact group action by a group G according to their rank.\nIf X has rank 1, then it displays hyperbolic dynamics: G has many free subgroups, G-periodic geodesics are dense,\nthe geodesic flow has a dense orbit...\nOn the other hand, if X has higher rank, then it carries special geometry:\nit must be isometric to a symmetric space or a euclidean building or split as a product.\nIn the talk, I will discuss the conjecture and report on recent progress.\n
SUMMARY:CAT(0) spaces of higher rank
CATEGORIES:Colloque / Congrès / Forum
LOCATION:PER 08\, auditoire 2.52\, Chemin du Musée 3\, 1700 Fribourg
URL;VALUE=URI:https://agenda.unifr.ch/e/fr/13635
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