Submitted by rybu on Mon, 09/26/2011 - 18:45
The figure-8 knot is a lovely example of a knot in 3-dimensions. It's one of the simplest knots you can draw. The complement admits a hyperbolic structure of finite volume. And the hyperbolic structure is very nice -- it is the union of two regular ideal tetrahedra, moreover, the n-th face of tetrahedron 1 is glued to the n-th face of tetrahedron 2, with two of the gluing maps by right-handed 2π/3 twists, and two by left-handed 2π/3 twists. The complement of the figure-8 knot (thought of as a knot in the 3-sphere) fibers over the circle, and the fibre is a once-punctured torus.
Submitted by rybu on Tue, 06/14/2011 - 18:47
The most frequently asked question I get after a presentation in seminars is "how did you draw those pictures?"
For example, the main image in this slide
Submitted by rybu on Tue, 04/26/2011 - 16:59
One of the things I find pretty neat about the splicing operad is how much goes into it. It's a relatively complicated structure and I'm a little surprised there aren't many similar, related structures in the literature.
Submitted by rybu on Sat, 04/23/2011 - 16:58
Shortly after arriving as a postdoc at the University of Rochester I started getting results on the global topology of spaces of knots. This was, in a sense, the first topic I had wanted to work on for my dissertation. But I got stuck, and my Ph.D evolved to a different topic. At Rochester, sparked by Fred Cohen's curiosity, the project regained momentum.
Submitted by rybu on Wed, 09/29/2010 - 16:55
One afternoon I was sitting around with Paolo Salvatore, trying to prove that an operad of little cubes had no hope of acting on spaces of string links. I was certain the operad couldn't act and kept on insisting on it. Eventually Paolo came up with a proof. This post is about Paolo's idea.
Submitted by rybu on Wed, 08/18/2010 - 16:50
My take, written up here.

Submitted by rybu on Tue, 06/08/2010 - 16:36

Towards the end of June the University of Brisbane is hosting a conference on a subject which as the quote above suggests, is something of a barren landscape scattered with unsavory characters.
Submitted by rybu on Mon, 02/22/2010 - 15:35
IPMU (the Institute for the Physics and Mathematics of the Universe) officially opened its new building this week. Ben Burton and I were in Tokyo visiting and I took some photos.
Submitted by rybu on Sun, 09/21/2008 - 16:34
Submitted by rybu on Sun, 08/10/2008 - 16:33
The creative process for papers has always been murky to me. I rarely set out to write a particular type of paper. Quite often results appear as by-products of computations I'm working on for some other reason.
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