Save Kea!

Kea, whose actual name is Marni D. Shepheard, is a New Zealand physicist and blogger. Her blog, Arcadian Functor was really interesting and educational, and has morphed into Arcadian Omegafunctor, via blogs with intermediate names.

Kea works on the intersection of higher category theory and particle physics, which is niche mathematics combined with niche physics, and as a result has been out of a job for a long time. Marni’s a survivor though (a famous and celebrated survivor, who, together with Sonja Rendell, survived a mountaineering mishap which would have killed the vast majority of us) and she’s been publishing on viXra and continuing to do physics with no funding and often in total abject poverty. It appears to be taking its toll.

It came from K2

At the “Mathematics of Knots 5″ conference at Waseda University, I attended a most interesting talk by Takefumi Nosaka. Nosaka’s work always gives me the impression of being robust and sophisticated, and this talk was no exception. This time he was in the process constructing new topological invariants of links as images of longitudes in of a ring.

ICERM Fall 2013: Topology, geometry, and dynamics

I’ve mentioned before that the fall semester program at ICERM for 2013 will focus on computation in low-dimensional topology, geometry, and dynamics.   You can now apply to be a long-term visitor for this as a graduate student, postdoc, or other.   The deadline for the postdoctoral positions is January 14, 2013; the early deadline for everyone else is December 1, 2012 and the second deadline March 15, 2013.

There will also be three week-long workshops associated with this, so mark your calendars for these exciting events:

1. Exotic Geometric Structures. September 15-20, 2013.
2. Topology, Geometry, and Group Theory: Informed by Experiment. October 21-25, 2013.
3. Geometric Structures in Low-Dimensional Dynamics. November 18-22, 2013.

The virtual Haken conjecture

Agol’s preprint, which includes a long appendix joint with Groves and Manning, is now on the arXiv.

Agol’s work on the Virtual Haken Conjecture

Over at Geometry and the Imagination, Danny Calegari is reporting live from Paris on talks by Agol and Manning on the announced proof of the VHC:  Part I, Part II, Part III. 

Bar-Natan – Dancso paper comes with seminar and video

Dror Bar-Natan makes the following announcement:

Dear Friends,

With help from my students, in the next semester I will be running the “wClips Seminar”, which will be a combination of a class, a seminar, and an experiment. We will meeting on Wednesdays at noon starting January 11, 2012 – follow us on http://www.math.toronto.edu/drorbn/papers/WKO/!

The “class” part of this affair is that we will slowly and systematically go over my in-progress joint paper with Zsuzsanna Dancso, “Finite Type Invariants of W-Knotted Objects: From Alexander to Kashiwara and Vergne” (short “WKO”, and again see http://www.math.toronto.edu/drorbn/papers/WKO/), section by section, lemma by lemma, and covering all necessary prerequisites as they arise.

The “seminar” component is the usual. Occasionally people other than me will be telling the story.

The “experiment” part is that every lecture will be video taped and every blackboard will be photographed and everything will be immediately put on the WKO website, so that at the end we will have along with the paper a “video companion” – series of video clips explaining every bit of it. The paper will be mathematically self-contained, yet in addition every section thereof will include a link/reference to the corresponding clip in its video companion. And every video clip will have its written counterpart in one of the sections of the paper.

Feel free to follow almost in real time! Also, please let me know if you want to be added to the wClips mailing list.

Best,

Dror.

Knot Theory gets major newspaper coverage!

On Friday, June 17, Japan’s second most-read newspaper, Asahi Shimbun, ran a full-page story on Knot Theory!!! Because of the sudden media exposure, I’ve been getting e-mails from family in Japan like studying Knot Theory makes me some kind of a celebrity. I’m sure it’s the same for every Knot Theorist who’s lived there- we’re enjoying our 15 minutes of fame right now.
The story is occasioned by the release of a fun computer game based on a theorem of Ayaka Shimizu. Ayaka is a member of Akio Kawauchi’s Knot Theory group at OCAMI. The theorem appears in her preprint Region crossing change is an unknotting operation.

Is knot theory `obvious but hard’?

Recently, there was a soft question on MathOverflow asking for examples of theorems which are `obvious but hard to prove’. There were three responses concerning pre-1930 knot theory, and I didn’t agree with any of them. This led me to wonder whether there might be a bit of a consensus in the mathematical community that knot theory is really much more difficult than it ought to be; and that good knot theory should be all about combinatorics of knot diagrams. And so knot colouring becomes `good knot theory’ for what I think are all the wrong reasons.

Slice-Ribbon Conjecture in danger!

A few days ago, I found gold in my inbox.
It was in a mass-mailing by Geometry & Topology Publications, announcing seven new papers. It was one of these, Fibered knots and potential counterexamples to the Property 2R and Slice-Ribbon Conjectures by Bob Gompf, Martin Scharlemann and Abigail Thompson, which really blew me away.
The paper is a gripping read. As I see things, its breakthrough result is the discovery of a family of slice knots which are unlikely to be ribbon, bringing my confidence in the veracity of the Slice-Ribbon Conjecture down from around 60% (what can I say? I was an optimist!) to around 5%. After more than 30 years, the Slice-Ribbon Conjecture is encircled and in imminent fear of annihilation.

Labeling figures in LaTeX

It’s been pretty quiet here on this modest blog, so I’m taking that as an excuse to blog about TeX. One of the fun things about being a low-dimensional topologist is that our papers have many pictures. This leads to the problem of how to add labels to these figures. The right way to do this, I’m convinced, is to do so within the TeX file itself so that the fonts match the body text and it’s easy to move/change the labels without access to the program that originally generated the image files. Colin Rourke’s pinlabel.sty is a good way to do this and is used by the MSP journals such as G&T. The hard part is figuring out the coordinates for the labels without a lot of guesswork. Pete Storm wrote pinlabeler which makes this trivially easy, but unfortunately it doesn’t work naturally with Mac OS X. Therefore I wrote labelpin which is less sophisticated than pinlaber, but works on both OS X and Linux (and probably within Cygwin or MSYS on Windows). It’s just a simple Python script, so there’s no need to compile anything, and on OS X all you should need to do is put it in your path and make it executable (“chmod +x labelpin”).

Alternatives to pinlabel.sty include overpic, WARMReader, and the import environment of xypic. It’s easy to modify the labelpin script to handle any of these, though generally pinlabel is the best package out there. (The only negative of pinlabel is that it requires you have an EPS version of the image file even if you’re using PDFLaTeX, and it can’t handle bitmapped files like PNG or JPG even though PDFLaTeX can. In contrast, I have some macros that work with xypic which can deal with such things, see my script labelxy for details).