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 Liouville illiouminated
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 You can solve the cube – with commutators!
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 Surface subgroups of Sapir’s group
 Upper curvature bounds and CAT(K)
 Bill Thurston 19462012
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 Agol’s Virtual Haken Theorem (part 3): return of the hierarchies
 Agol’s Virtual Haken Theorem (part 2): AgolGrovesManning strike back
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Author Archives: Danny Calegari
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
Div, grad, curl and all this
The title of this post is a nod to the excellent and wellknown Div, grad, curl and all that by Harry Schey (and perhaps also to the lesserknown sequel to one of the more consoling histories of Great Britain), and the purpose … Continue reading
Posted in 3manifolds, Riemannian geometry
Tagged curl, div, exposition, grad, Riemannian geometry, vector field
9 Comments
A tale of two arithmetic lattices
For almost 50 years, Paul Sally was a towering figure in mathematics education at the University of Chicago. Although he was 80 years old, and had two prosthetic legs and an eyepatch (associated with the Type 1 diabetes he had his … Continue reading
Posted in Hyperbolic geometry, Number theory
Tagged arithmetic lattice, Hyperbolic geometry, orthogonal group
2 Comments
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
Kähler manifolds and groups, part 1
One of the nice things about living in Hyde Park is the proximity to the University of Chicago. Consequently, over the summer I came in to the department from time to time to work in my office, where I have … Continue reading