Amenability and fixed point properties
Introductory Workshop: Geometric Group Theory August 22, 2016 - August 26, 2016
Location: MSRI: Simons Auditorium
geometric group theory
Kazhdan's property T
negative curvature manifolds
mapping class groups
von Neumann-Day conjecture
20F65 - Geometric group theory [See also 05C25, 20E08, 57Mxx]
20F06 - Cancellation theory; application of van Kampen diagrams [See also 57M05]
37F30 - Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems
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 non-positively 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)
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