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# Superintrinsic synthesis in fixed point properties

## Amenability, coarse embeddability and fixed point properties December 06, 2016 - December 09, 2016

December 08, 2016 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Masato Mimura (Tohoku University)
Location: MSRI: Simons Auditorium
Tags/Keywords
• fixed point properties

• property (T)

• property t

• expander graph

• bounded generation

• hyperbolic groups and generalizations

• Banach space

• group cohomology

• index theory

• non-commutative geometry

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

#### 14648

Abstract

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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