Superintrinsic synthesis in fixed point properties
Amenability, coarse embeddability and fixed point properties December 06, 2016 - December 09, 2016
Location: MSRI: Simons Auditorium
fixed point properties
property (T)
property t
expander graph
bounded generation
hyperbolic groups and generalizations
Banach space
group cohomology
index theory
non-commutative geometry
37A15 - General groups of measure-preserving transformations [See mainly 22Fxx]
43-XX - Abstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx}
46-XX - Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx}
57-XX - Manifolds and cell complexes {For complex manifolds, see 32Qxx}
20F65 - Geometric group theory [See also 05C25, 20E08, 57Mxx]
14648
The following natural question arises from Shalom's innovational work (1999, Publ.IHES) on Kazhdan's property (T). ``Can we establish an `intrinsic' criterion to synthesize relative fixed point properties into the whole fixed point property without assuming `Bounded Generation'?'' This talk is aimed to present a resolution to this question in the affirmative. Our criterion works for ones with respect to certain classes of Busemann Non-Positively Curved spaces. It, moreover, suggests a further step toward constructing super-expanders from finite simple groups of Lie type.
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14648
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