Conference on Higher Gauge Theory, Quantum Gravity, and Topological Field Theory December 18, 2010
Posted by Chris Schommer-Pries in mathematical physics, QFT, quantum topology, talks, tqft, Uncategorized.Tags: tqft
1 comment so far
In February there is going to be a workshop and school dedicated to exploring the interactions of Quantum Gravity, Higher Gauge Theory, and Topological Field Theory. I’m excited about the chance to share ideas and hopefully create some new mathematics.
The conference will take place in Lisbon, Portugal, and yours truly will be giving one of the mini-courses for the school (the topic is going to be the classification of extended 2D tqfts, something near and dear to my heart). Of course that makes me really excited, but I am also excited about the other topics too and I think the mix of ideas will be invigorating. For more info look below the break.
Artin-Wedderburn in fusion categories December 16, 2010
Posted by Noah Snyder in fusion categories, quantum algebra.2 comments
In quantum algebra we’re often studying some classical algebraic notion, but instead of working in the category of vector spaces you instead work in a more general tensor category. For example, the theory of finite type knot invariants is roughly the theory of simple Lie algebra objects in symmetric tensor categories, while the theory of subfactors is roughly that of simple algebra objects in unitary tensor categories. The basic question is then which notions from the classical theory generalize to the quantum setting. For example, is there an analogue of Artin-Wedderburn for semisimple algebra objects in fusion categories? The goal of this post is to argue that the following theorem (due to Ostrik, modulo any errors I’ve introduced) gives a satisfactory generalization.
Any semisimple algebra object in a fusion category
is isomorphic (as an algebra object) to the internal endomorphisms End(X) for some object X in a semisimple module category
over
First I’ll unpack the definitions in this statement and then I’ll explain how Artin-Wedderburn for semisimple algebras over a fixed field k follows from this statement. I’ve been thinking about this theorem because Pinhas Grossman and I have been using it to classify “quantum subgroups” of the Haagerup fusion categories, but that’s a story for another day.
(more…)
The decline of quantum algebra (QA) December 14, 2010
Posted by Joel Kamnitzer in quantum algebra, things I don't understand.20 comments
I was browsing through different category listings on the arXiv today and noting the changes in numbers of papers over the years. As you might expect, there are more and more papers being posted to the arXiv every year. However, one category defies this trends: QA (quantum algebra).
There are actually less papers being posted to QA in the past three years (2010 317, 2009 308, 2008 323), than there were in the late 90s (1998 364, 1997 434, 1996 395). By contrast, there are about 4 times as many AG papers in the past few years compared to the late 90s, about 10 times as many RT papers, and about 5 times as many GT papers.
What do you make of this? Does it represent a trend in the kind of math that people are doing? Or are people just classifying their work differently?
It would be interesting to see if one can use this arXiv category to get a sense of which fields are becoming more and less popular over time.
What would be an ideal system through which amateurs can advertise their results? December 11, 2010
Posted by Ben Webster in guest post, math life, websites.10 comments
(this is a guest post by Theo Johnson-Freyd)
Occasionally on MathOverflow (and elsewhere on and off the internet), amateur mathematicians try to advertise their research results and solicit feedback from professionals. For example, recently HH Hannett (who holds a long-ago BS in mathematics, but has been doing non-math engineering work for many years) asked a well-meaning but inappropriate-for-the-forum question about Where to submit a recent paper, and how to cope with the negative or dismissive responses received from a previous journal submission. In a comment on a subsequent (now-deleted) post, Hannett wished “that there might be a mechanism whereby amateur (“non-PhD”) contributions can get a fair shake …. Perhaps some sort of delegated, tiered system that a paper has to survive.”
Discussing whether/what/how such a system should exist/be like/be set up is, to my mind, valuable. A potential answer is that the existing peer-review process is already adequate. I could certainly believe that the best answer is “no change necessary”: I’m young enough that I don’t really know the full extent of the current system; maybe we should just continue to avoid the cranks. But most amateurs don’t want to waste professionals’ time — they want to do math, and for the same reason (it’s fun!) that professionals do, and the current academic system, clearly, does not provide sufficient outlets for well-meaning amateurs (or “cranks” wouldn’t be a problem).
My hope with this post, then, is to constructively generate some ideas for relieving this pressure. In particular, it’s all well and good to ask that amateurs learn and follow reasonable advice, but my goal is to come up with things that professionals can do (pro)actively. These ideas could range from the fantastical (design a better peer-review system! establish free universal advanced mathematics education!) to the specific (make “respond to amateurs” part of universities’ “service” requirements!). An important note: My goal is not to establish yet another thread in which we can swap stories of all the dumb things amateurs have sent us. That’s certainly a fun game, but there are other outlets for it.
So, netizens: What, specifically, are the weaknesses and strengths of the current system when it comes to amateur mathematics? What would
be an ideal system through which amateur mathematicians could advertise their work and solicit feedback? How can professional
mathematicians help to set up such a system?
(this is an addendum by Ben)
Maybe I should save this for the comments, but I can’t resist abusing my blog privileges and throwing out an idea. I don’t think that any system that require a lot of input from people on the usual professional mathematics track is likely to succeed; it’s hard enough to get them to seriously read each other’s papers (for example, I’d much rather see a system whereby graduate students can read and give feedback on each other’s papers than one where they read amateur mathematicians). But perhaps we can ask amateurs to review each other’s work.
One could have a website where anyone can upload preprints and then give people function to vote on the preprints, write reviews and vote on the reviews. The power of your vote could be regulated using a page-rank type system where you only get real voting power as other people vote up your work. This wouldn’t have to restricted to amateurs only, but it’s hard for me to imagine it catching on quickly with professionals. Of course, it’s hard to know whether it would attract a big enough and diverse enough user base to effectively sort through papers, but you never know, it might.
Postdoc at Oregon December 9, 2010
Posted by Ben Webster in jobs.1 comment so far
Usually I wouldn’t bother to announce this here, but since the ad is going up (IMHO) extremely late in the season, I thought I would let people know that we will be hiring for a 3-year postdoc position at Oregon this year. It was posted on MathJobs today. There’s no limit in terms of subject aside being “of interest to the department.” Feel free to email me if you want more information.
