Cornell has created a tribute page to Bill Thurston with links to biographical information and remembrances. (Tim Riley posted this in the comments on Nathan’s post, but I wanted to make sure everyone saw it.) Thurston’s work is certainly fundamental to most of the mathematics that I think about (see, for example, this post) but just as important is what he contributed to mathematical culture and community. If you haven’t read On Proof and Progress in Mathematics, you should (and if you haven’t read it recently, you should read it again). I have always been proud to be part of a field where someone as kind, generous and selfless as Bill Thurston could become one of the leading and most prominent figures. He will be deeply missed.
Tomorrow, on Monday July 16th from 25:23 to 25:53 (i.e. July 17th from 1:23-1:53 AM), Fuji Television will screen an episode of “Takeshi Kitano presents Comaneci University Mathematics” focussing on Knot Theory! Although not exactly at a prime time slot, this is an Emmy nominated popular TV series. It will be focussed on Kouki Taniyama’s Knot Theory seminar at Waseda University, and they will have permission to upload clips to Kouki Taniyama’s homepage after the episode has been screened. This is major media exposure. One hopes that the ratings will be as high as possible, and that other TV stations in other countries will catch on to the fact that low dimensional topology makes good television.
The best exposure low dimensional topology ever got in Japan, I think, was NHK’s 2007 Special Why the 100-year-old conjecture was proven about Perelman, Geometrization, and the Poincaré Conjecture. This documentary told a compelling story to people with no mathematical background, to entertain instead of to educate. There was virtually no gossip in it (unlike media coverage of the topic in Russia, for example), and the real hero was the mathematics. At the dramatic climax, you feel like shouting out “Of course! The key missing idea is differential geometry on Alexandrov spaces!!” without necessarily knowing what any of those words mean. It’s just very good television. I couldn’t find it online (it’s in Japanese anyway, so inaccessible for most readers without a translation) because it’s copywrited material, but I did find this video which, despite being heavily edited, gives some flavour of what it was like. (more…)
Gil Kalai, my old Graph Theory professor at Hebrew University, and a great mathematical inspiration, who won the Rothschild Prize a few weeks ago (congratulations Gil!), wrote a very nice blog post about another massive recent result in low dimensional topology.
Some nights, one gazes up at the stars, and thinks about philosophy. Who are we? What is the meaning of life? What is reality? What are manifolds really?
This morning, I looked at Poincaré’s original definition in Papers on Topology: Analysis Situs and Its Five Supplements, translated by John Stillwell. His original definition was pretty-much that a manifold is a quotient of by a properly discontinuous group action, that group being his original fundamental group. Implicitly, his smooth, PL, and topological categories were all the same thing (indeed true for 1-manifolds, and for dimensions 2 and 3 PL and smooth categories still “coincide” in a sense that can be made fully precise); nowadays we understand that the situation is more subtle. But I’m still not sure that I understand what a manifold is- what it really is.
In some non-mathematical, philosophical (theological?) sense, I believe that both smooth and PL manifolds actually exist, in the sense that natural numbers exist, and tangles exist. Our clumsy formal definitions are attempts at describing something that is actually out there, as the Peano axioms describe the natural numbers. I also believe that Physics is a guide to Mathematics, because things that really exist might also be observed… so ideas from Physics (topological invariants defined by means of path integrals) ought to be taken very seriously, and it is my irrational belief that these will eventually turn out to be the most fundamental invariants in some precise mathematical sense.
It is fascinating to me, then, that input from physics seems to be leading towards a fundamental rethink of the basic definitions of smooth and PL manifolds. I feel like we had some sub-optimal definitions, which we worked with for sociological reasons (definitions are made by people, and people are not perfect), and maybe in the not too distant future there will be a chance to put more convenient definitions in place. Maybe the real world (physics) will force it on us. Let me tell you, then, about some of the papers I’ve been (casually) flicking through recently (the one I’m most excited about is Kirillov’s On piecewise linear cell decompositions). (more…)
Scott Morrison (of Secret Blogging Seminar) and Andrew Stacey (of the nLab) have created a discussion forum called Math 2.0 to discuss the future of mathematics publishing: Should journals continue to exist? If so what should they be like? What roles will other types of publishing (arXiv, blogs, wikis, MathOverflow, etc.) play in the future landscape? Clearly, this is an important conversation to have – The major role that journals still play (as I see it) is to provide non-experts with a means of assessing and comparing mathematicians, areas within mathematics and even mathematics relative to other fields. Hiring and tenure decisions and agency funding decisions, to name just two, require a system of vetting (to borrow a term from politics) that administrators can understand and believe they can trust. The one strength of the current system is that it has a sense of legitimacy (at least to outsiders.) It seems that we, as a community, now have an opportunity to change the system, or perhaps even create a new one. I hope that the discussions on Math 2.0 will help ensure that the new system is fair and effective, but also a system that will be deemed legitimate by non-mathematicians.
I recently discovered that Siddhartha Gadgil is using google+ as a sort of topology (mini?)blog. His posts are all public, so you don’t need a google account to view them. He currently has a number of videos describing Stalling’s topological proof of Grushko’s Theorem: Part 1, Part 2, Part 3.
(I don’t know how to link to a specific post, rather than to the whole stream.) Are you using google+ as a blogging platform? Do you know of any other topologists who are? If so, leave a comment. In fact, if you’ve discovered any new topology blogs that aren’t on our (outdated) blogroll, feel free to post a comment about that as well.
Mathematicians have been complaining for years about Elsevier‘s business practices. In 2006, topologists rose up against it, when the editorial board of Topology resigned and established the Journal of Topology.
A few days ago, Tim Gowers wrote a blog post HERE suggesting that it might now be a good time to act together to stop Elsevier by refusing to submit to their journals or to referee or do editorial work. A petition is HERE.
As a random thought, I wonder whether it would be possible for representatives of the scientific community to sue large publishers to gain open access to papers written before year X, where X is around 2005 or something.
I just added two student oriented conferences to the LDTopology conference list, which I think deserve special attention. The first is the UnKnot conference, which is specifically intended for undergraduate students. Since I don’t think many undergraduates look at the conference page (or read this blog at all for that matter), you should encourage any promising students that you know to consider going. Since Colin Adams is one of the organizers, it promises to be fun.
The second conference is the Topology Student Workshop at Georgia Tech, which appears to be intended for graduate students. It looks like this one is going to have a lot of professional development, which is becoming more and more important these days. A few years ago, there was an apparently unrelated “Topology Student Forum” at Tulane University. I think they had plans of making it an annual event, but I couldn’t find any references to a 2012 meeting. If anyone has information about this (or any other upcoming topology conference), please leave a comment on this page or on the conferences page.
Update: Right after I posted this, I found out about two other student conferences. The first is the Graduate Student Topology Conference at Indiana University, March 31-April 1st. The second is the Underrepresented Students in Topology and Algebra Research Symposium (USTARS) at University of Iowa, April 13-15.
The VU University Amsterdam is planning a restructuring that will eliminate the geometry and topology group, eliminating four tenured faculty. The Secret Blogging Seminar has posted a letter from Tilman Bauer explaining the situation. You can read and sign the petition here. If the petition shows the univeristy that this action will be highly publicized and cause permanent damage to their reputation, they may be forced to reconsider.
It took a while, but the registration form (which includes requesting travel support) for the Geometry and Topology Down Under conference is now open. I thought this deserved a blog post because the deadline for funding is soon – Monday, April 18th. You can find the conference web page on the LDTopology conference list (in the upper right hand corner of the blog web page) or by clicking here.