Category Archives: Dynamics

Filling geodesics and hyperbolic complements

Patrick Foulon and Boris Hasselblatt recently posted a preprint entitled “Nonalgebraic contact Anosov flows on 3-manifolds”. These are flows which are at the same time Anosov (i.e. the tangent bundle splits in a flow-invariant way into stable, unstable and flow directions) and contact … Continue reading

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Quasigeodesic flows on hyperbolic 3-manifolds

My student Steven Frankel has just posted his paper Quasigeodesic flows and Mobius-like groups on the arXiv. This heartbreaking work of staggering genius interesting paper makes a deep connection between dynamics, hyperbolic geometry, and group theory, and represents the first significant progress … Continue reading

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Ziggurats and the Slippery Conjecture

A couple of months ago I discussed a method to reduce a dynamical problem (computing the maximal rotation number of a prescribed element  in a free group given the rotation numbers of the generators) to a purely combinatorial one. Now Alden Walker … Continue reading

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Rotation numbers and the Jankins-Neumann ziggurat

I’m in Melbourne right now, where I recently attended the Hyamfest and the preceding workshop. There were many excellent talks at both the workshop and the conference (more on that in another post), but one thing that I found very interesting … Continue reading

Posted in 3-manifolds, Dynamics | Tagged , , | 5 Comments

Harmonic measure

An amenable group acting by homeomorphisms on a compact topological space preserves a probability measure on ; in fact, one can given a definition of amenability in such terms. For example, if is finite, it preserves an atomic measure supported … Continue reading

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Faces of the scl norm ball

I am in Melbourne at the moment, in the middle of giving a lecture series, as part of the 2009 Clay-Mahler lectures (also see here). Yesterday I gave a lecture with the title “faces of the scl norm ball”, and … Continue reading

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van Kampen soup and thermodynamics of DNA

The development and scope of modern biology is often held out as a fantastic opportunity for mathematicians. The accumulation of vast amounts of biological data, and the development of new tools for the manipulation of biological organisms at microscopic levels … Continue reading

Posted in Biology, Dynamics, Groups | Tagged , , , , , , , | 4 Comments