Author Archives: Danny Calegari

Bing’s wild involution

Everyone knows that Alexander proved that the 3-sphere is irreducible; i.e. that every smoothly embedded 2-sphere bounds a ball on both sides. Everyone also knows that he showed that one cannot remove the hypothesis `smooth’ altogether, since at about the … Continue reading

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Stiefel-Whitney cycles as intersections

This quarter I’m teaching the “Differential Topology” first-year graduate class, and for a bit of fun, I decided to teach an introduction to characteristic classes, following the classic book of that name by Milnor and Stasheff. The book begins with … Continue reading

Posted in Algebraic Topology | Tagged , , , , , , , | 7 Comments

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 , , , , , | 6 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 , , , , , | 2 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

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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