Category Archives: Hyperbolic geometry

Schläfli – for lush, voluminous polyhedra

Because of some turbulence in real life (™) over the last few months, it’s been somewhat hard to concentrate on research. Fortunately the obligation of teaching sometimes exerts the right sort of psychological pressure to keep my mind on mathematics in short bursts. Continue reading

Posted in 3-manifolds, Hyperbolic geometry, Special functions | Tagged , , , , , | 4 Comments

Mr Spock complexes (after Aitchison)

The recent passing of Leonard Nimoy prompts me to recall a lesser-known connection between the great man and the theory of (cusped) hyperbolic 3-manifolds, observed by my friend and former mentor Iain Aitchison. In particular, I am moved to give a brief presentation … Continue reading

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Roots, Schottky semigroups, and Bandt’s Conjecture

It has been a busy quarter. Since August, I have made 10 trips, to conferences or to give colloquia. On 8 out of the 10 trips, I talked about a recent joint project with Sarah Koch and Alden Walker, on a topic in … Continue reading

Posted in Complex analysis, Dynamics, Hyperbolic geometry, Number theory | Tagged , , , , , , , , , , , , , | 1 Comment

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 , , , , , , , | 7 Comments

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 , , , , , | 2 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

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