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Tag Archives: scl
Polygonal words
Last Friday, Henry Wilton gave a talk at Caltech about his recent joint work with Sang-hyun Kim on polygonal words in free groups. Their work is motivated by the following well-known question of Gromov: Question(Gromov): Let be a one-ended word-hyperbolic group. … Continue reading
Posted in Groups, Surfaces
Tagged double of free group, ends, Henry Wilton, hyperbolic groups, roundoff trick, Sang-hyun Kim, scl, Stallings theorem on ends, surface subgroup
6 Comments
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
1 Comment
scl, sails and surgery
I have just uploaded a paper to the arXiv, entitled “Scl, sails and surgery”. The paper discusses a connection between stable commutator length in free groups and the geometry of sails. This is an interesting example of what sometimes happens … Continue reading
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
4 Comments
Quasimorphisms and laws
A basic reference for the background to this post is my monograph. Let be a group, and let denote the commutator subgroup. Every element of can be expressed as a product of commutators; the commutator length of an element is the … Continue reading
five week plan
As an experiment, I plan to spend the next five weeks documenting my current research on this blog. This research comprises several related projects, but most are concerned in one way or another with the general program of studying the … Continue reading
Posted in Overview
Tagged Gromov's question, hyperbolic groups, scl, stable commutator length, surface groups
4 Comments
Geometry and the imagination 