Irreducible group actions by affine isometries on Hilbert spaces
Amenability, coarse embeddability and fixed point properties December 06, 2016 - December 09, 2016
Location: SLMath: Eisenbud Auditorium
Unitary representations
affine actions on Hilbert spaces
Amenability
a-T-menability
expander graph
index theory
non-commutative geometry
fixed point properties
hyperbolic groups
Banach space
functional analysis
group cohomology
20K40 - Homological and categorical methods for abelian groups
00A35 - Methodology of mathematics {For mathematics education, see 97-XX}
00B25 - Proceedings of conferences of miscellaneous specific interest
00B55 - Collections of translated articles of miscellaneous specific interest
01-11 - Research data for problems pertaining to history and biography
20E15 - Chains and lattices of subgroups, subnormal subgroups [See also 20F22]
14639
Important classes of locally compact groups are characterized by their actions by affine isometries on Hilbert spaces (groups with Kazhdan's property, a-T-menable groups aka groups with the Haagerup property). We will be interested on the question of irreducibility of such actions, in the sense that the only non empty closed invariant affine subspace is the whole space. This notion was extensively studied in a recent joint work of T. Pillon, A. Valette and myself. We will report on this work as well as on some further results. Special attention will be paid to affine actions whose linear part is a factorial representation, that is, a representation which generates a factor in the von Neumann algebra sense
bekka Notes
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