Author Archives: Danny Calegari

Mapping class groups: the next generation

Nothing stands still except in our memory. – Phillipa Pearce, Tom’s Midnight Garden In mathematics we are always putting new wine in old bottles. No mathematical object, no matter how simple or familiar, does not have some surprises in store. My … Continue reading

Posted in Dynamics, Groups, Hyperbolic geometry, Surfaces | Tagged , , , , , , , | Leave a comment

Groups quasi-isometric 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

Posted in 3-manifolds, Complex analysis, Groups, Hyperbolic geometry, Uncategorized | Tagged , , , , , | Leave a comment

Div, grad, curl and all this

The title of this post is a nod to the excellent and well-known Div, grad, curl and all that by Harry Schey (and perhaps also to the lesser-known sequel to one of the more consoling histories of Great Britain), and the purpose … Continue reading

Posted in 3-manifolds, Riemannian geometry | Tagged , , , , , | 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 , , | 2 Comments

3-manifolds everywhere

When I started in graduate school, I was very interested in 3-manifolds, especially Thurston’s geometrization conjecture. Somehow in dimension 3, there is a marvelous marriage of flexibility and rigidity: generic 3-manifolds are flexible enough to admit hyperbolic structures — i.e. Riemannian metrics … Continue reading

Posted in 3-manifolds, Groups, Hyperbolic geometry | Tagged , , , , | Leave a comment

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

Posted in Groups, Hyperbolic geometry, Visualization | Tagged , | 3 Comments

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

Posted in Algebraic Geometry, Complex analysis, Geometric structures, Groups | Tagged , , , , , , , , | Leave a comment