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 , , , , , , , , | 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 , , , , , , , , , | 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

Posted in Convex geometry, Groups | Tagged , , , , , , , , , | 1 Comment

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

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

Posted in Groups | Tagged , , , , | 3 Comments

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 , , , , | 4 Comments