Author Archives: Danny Calegari

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

Slightly elevated Teichmuller theory

Last week at my invitation, David Dumas spoke in the U Chicago geometry seminar and gave a wonderful introductory talk on the theory of convex real projective structures on surfaces. This is the first step on the road to what is colloquially known … Continue reading

Posted in Complex analysis, Geometric structures, Projective geometry, Surfaces | Tagged , , , , , | Leave a comment

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

Taut foliations and positive forms

This week I visited Washington University in St. Louis to give a colloquium, and caught up with a couple of my old foliations friends, namely Rachel Roberts and Larry Conlon. Actually, I had caught up with Rachel (to some extent) … Continue reading

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Explosions – now in glorious 2D!

Dennis Sullivan tells the story of attending a dynamics seminar at Berkeley in 1971, in which the speaker ended the seminar with the solution of (what Dennis calls) a “thorny problem”: the speaker explained how, if you have N pairs of … Continue reading

Posted in Dynamics, Psychology, Visualization | Tagged , , , , , , | 3 Comments

Dipoles and Pixie Dust

The purpose of this blog post is to give a short, constructive, computation-free proof of the following theorem: Theorem: Every compact subset of the Riemann sphere can be arbitrarily closely approximated (in the Hausdorff metric) by the Julia set of … Continue reading

Posted in Complex analysis, Dynamics | Tagged , , | 6 Comments