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Author Archives: Danny Calegari
Random groups contain surface subgroups
A few weeks ago, Ian Agol, Vlad Markovic, Ursula Hamenstadt and I organized a “hot topics” workshop at MSRI with the title Surface subgroups and cube complexes. The conference was pretty well attended, and (I believe) was a big success; … Continue reading
wireframe, a tool for drawing surfaces
The purpose of this brief blog post is to advertise that I wrote a little piece of software called wireframe which can be used to quickly and easily produce .eps figures of surface for inclusion in papers. The main use is … Continue reading
Cube complexes, Reidemeister 3, zonohedra and the missing 8th region
There is an old puzzle which starts by asking: what is the next number in the sequence 1,2,4,? We are supposed to recognize the start of the sequence and answer that the next number is surely 8, because the first … Continue reading
Orthocentricity
Last week while in Tel Aviv I had an interesting conversation over lunch with Leonid Polterovich and Yaron Ostrover. I happened to mention the following gem from the remarkable book A=B by Wilf-Zeilberger. The book contains the following Theorem and … Continue reading
Kenyon’s squarespirals
The other day by chance I happened to look at Richard Kenyon’s web page, and was struck by a very beautiful animated image there. The image is of a region tiled by colored squares, which are slowly rotating. As the … Continue reading
Thurston talks on geometrization at Harvard
In winter and spring of 2001, Nathan Dunfield and I ran a seminar at Harvard whose purpose was to go through Thurston’s proof of the geometrization theorem for Haken manifolds. This was a very useful and productive exercise, and there … Continue reading
Random turtles in the hyperbolic plane
My eldest daughter Lisa recently brought home a note from her school from her computer class teacher. Apparently, the 5th grade kids have been learning to program in Logo, in the MicroWorlds programming environment. I have very pleasant memories of … Continue reading
