Amenability and fixed point properties
Introductory Workshop: Geometric Group Theory August 22, 2016  August 26, 2016
Location: SLMath: Eisenbud Auditorium
geometric group theory
hyperbolic group
amenable groups
Kazhdan's property T
negative curvature manifolds
Banach space
expander graph
mapping class groups
von NeumannDay conjecture
20Jxx  Connections of group theory with homological algebra and category theory
00A35  Methodology of mathematics {For mathematics education, see 97XX}
35R02  PDEs on graphs and networks (ramified or polygonal spaces)
14597
A fundamental dichotomy in the theory of infinite groups is the one between amenable groups and groups with Kazhdan's Property (T). In this talk I shall overview versions of these two opposite properties, connections to actions on nonpositively curved spaces and on Banach spaces, to other geometric features of the groups, and to expander graphs. I shall also mention what is known in the setting of random groups and that of important classes of infinite groups (e.g. lattices, mapping class groups, Out(F_n) etc)
Drutu Notes

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