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Category Archives: Dynamics
Filling geodesics and hyperbolic complements
Patrick Foulon and Boris Hasselblatt recently posted a preprint entitled “Nonalgebraic contact Anosov flows on 3manifolds”. These are flows which are at the same time Anosov (i.e. the tangent bundle splits in a flowinvariant way into stable, unstable and flow directions) and contact … Continue reading
Quasigeodesic flows on hyperbolic 3manifolds
My student Steven Frankel has just posted his paper Quasigeodesic flows and Mobiuslike 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
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
Posted in Dynamics
Tagged Arnol'd tongues, combinatorics, Rigidity, rotation number, ziggurats
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Rotation numbers and the JankinsNeumann 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
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
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 ClayMahler lectures (also see here). Yesterday I gave a lecture with the title “faces of the scl norm ball”, and … Continue reading
Posted in Dynamics, Groups, Surfaces
Tagged Bavard duality, free groups, immersions, maximal representation, quasimorphisms, Rigidity, rotation number, scl, Surfaces, Symplectic geometry
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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 biological computation, DNA, fatgraphs, free groups, Holliday junction, scl, thermodynamics, van Kampen diagrams
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