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 Liouville illiouminated
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 You can solve the cube – with commutators!
 Chiral subsurface projection, asymmetric metrics and quasimorphisms
 Random groups contain surface subgroups
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 Surface subgroups of Sapir’s group
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 Bill Thurston 19462012
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Category Archives: Groups
Groups quasiisometric to planes
I was saddened to hear the news that Geoff Mess recently passed away, just a few days short of his 54th birthday. I first met Geoff as a beginning graduate student at Berkeley, in 1995; in fact, I believe he gave the … Continue reading
3manifolds everywhere
When I started in graduate school, I was very interested in 3manifolds, especially Thurston’s geometrization conjecture. Somehow in dimension 3, there is a marvelous marriage of flexibility and rigidity: generic 3manifolds are flexible enough to admit hyperbolic structures — i.e. Riemannian metrics … Continue reading
Posted in 3manifolds, Groups, Hyperbolic geometry
Tagged 3manifolds, acylindrical, quasiconvex group, Random groups, Sierpinski carpet
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kleinian, a tool for visualizing Kleinian groups
It’s been a while since I last blogged; the reason, of course, is that I felt that I couldn’t post anything new before completing my series of posts on Kähler groups; but I wasn’t quite ready to write my last … Continue reading
Kähler manifolds and groups, part 2
In this post I hope to start talking in a bit more depth about the global geometry of compact Kähler manifolds and their covers. Basic references for much of this post are the book Fundamental groups of compact Kähler manifolds by … Continue reading
You can solve the cube – with commutators!
After a couple years of living out of suitcases, we recently sold our house in Pasadena, and bought a new one in Hyde Park. All our junk was shipped to us, and the boxes we didn’t feel like unpacking are … Continue reading
Chiral subsurface projection, asymmetric metrics and quasimorphisms
Last week I was at Oberwolfach for a meeting on geometric group theory. My friend and collaborator Koji Fujiwara gave a very nice talk about constructing actions of groups on quasitrees (i.e. spaces quasiisometric to trees). The construction is inspired … Continue reading
Random groups contain surface subgroups
A few weeks ago, Ian Agol, Vlad Markovic, Ursula Hamenstadt and I organized a “hot topics” workshop at MSRI with the title Surface subgroups and cube complexes. The conference was pretty well attended, and (I believe) was a big success; … Continue reading