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Home » Topology Seminar: Zimmer's conjecture: subexponential growth, measure rigidity and strong property (T)

Seminar

Topology Seminar: Zimmer's conjecture: subexponential growth, measure rigidity and strong property (T) August 31, 2016 (04:10 PM PDT - 05:00 PM PDT)
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Location: 3 Evans Hall
Speaker(s) David Fisher (Indiana University)
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This talk is a sequel to the colloquium of August 25. I will try to make it logically independent and self-contained, but most of the history and motivation will occur in the colloquium talk and this talk will emphasize ideas of proofs of the following theorem. Let G be a cocompact lattice in SL(n,R) where n >3, M a compact manifold and a: G— > Diff(M) a homomorphism. If dim(M)< n-1, a(G) is finite. Furthermore if dim(M)=n-1and a(G) preserves a volume form, a(G) is finite. The proof has many surprising features, including that it uses hyperbolic dynamics to prove an essentially elliptic result and that it uses results on homogeneous dynamics, including Ratner's measure classification theorem, to prove results about inhomogeneous system. This is joint work with Aaron Brown and Sebastian Hurtado. (Hurtado is a recent Berkeley Ph.d.)  There will be a preparatory talk at 2 PM.  Those not familiar with Lyapunov exponents and homogeneous dynamics are encouraged to attend the preparatory talk.

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