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Tag Archives: Rigidity
Liouville illiouminated
A couple of weeks ago, my student Yan Mary He presented a nice proof of Liouville’s theorem to me during our weekly meeting. The proof was the one from Benedetti-Petronio’s Lectures on Hyperbolic Geometry, which in my book gets lots … Continue reading
Posted in Complex analysis, Euclidean Geometry, Rigidity
Tagged conformal map, Liouville's theorem, Rigidity, umbilical surface
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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
Posted in Dynamics
Tagged Arnol'd tongues, combinatorics, Rigidity, rotation number, ziggurats
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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
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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Geometry and the imagination 