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July 2, 2009
Open Access to Taxpayer-Funded Research
Posted by John Baez
-Café regulars will know about Representative Conyer’s bill that would repeal the National Institute of Health’s public access policy and forbid other US funding agencies from mandating open access to research papers written with the help of federal grant money. Conyers’ argument in favor of this bill was hilariously misinformed. He wrote: “Journal publishers organize and pay for peer review with the proceeds they receive from the sale of subscriptions to their journals.”
But laughing at the folly of the world is not really much fun. Now some good news, for a change! A bill has been introduced that would do quite the opposite. It would ensure free, timely, online access to the published results of research funded by the National Science Foundation and ten other US federal agencies!
Elsevier Pays for Favorable Book Reviews
Posted by John Baez
We all know how Elsevier has been running fake medical journals for the drug company Merck, devoted to saying good things about Merck products. But this isn’t all they’re up to.
For example, on a recent thread here at the -Café, Ben pointed out an interesting BBC news report. Apparently Elsevier offered Amazon gift certificates to academics who would write 5-star reviews of their textbook Clinical Psychology!
Caught red-handed, Elsevier blamed this action on an unnamed ‘rogue employee’. They did not say whether any disciplinary action would be taken.
July 1, 2009
Laubinger on Lie Algebras for Frölicher Groups
Posted by Urs Schreiber
[guest post by Martin Laubinger in the context of Smootheology: the study of generalized smooth spaces]
I have posted a preprint which contains the central new result I obtained in my
dissertation.
The result may not directly relate to higher category theory. Still, I would appreciate feedback and problems for further investigation:
Martin Laubinger
A Lie algebra for Frölicher groups
(arXiv)
Here is a short description: The category of Frölicher spaces is a cartesian closed category which contains the category of smooth finite-dimensional manifolds as a full subcategory. The same is true for the closely related category of diffeological spaces. However, it is easier to define tangent spaces to Frölicher spaces than to diffeological spaces. Many groups have natural Frölicher structures, including all Lie groups, but also certain groups of mappings such as or , which can not be given a manifold structure in general. A basic question is whether the tangent space (in the Frölicher sense) at the identity of these groups can be equipped with a Lie bracket. I have been able to construct such a Lie bracket, but there is an additional condition which has to be verified. This condition is very natural, but I have not found a general proof. In my thesis, I did not have an example for a group which satisfies the extra condition, but in the meantime I verified the condition for the additive group (product of the reals) if J is not too big. This is explained in detail in the preprint.
June 30, 2009
Springer Verlag Publishes ‘Proof’ of Goldbach’s Conjecture
Posted by John Baez
The ‘big three’ science publishers — Elsevier, Springer, and Wiley–Blackwell — like to argue that their high prices pay for high quality. Recent events cast a tinge of doubt on this. We all know about the case of El Naschie, and Elsevier’s fake medical journals. Now Springer has published a book that purports to contain elementary proofs of Fermat’s Last Theorem and Goldbach’s Conjecture!
Here it is:
- Nico F. Benschop, Associative Digital Network Theory: An Associative Algebra Approach to Logic, Arithmetic and State Machines, Springer Verlag, 2009. ISBN: 978-1-4020-9828-4.
June 26, 2009
This Book Needs a Title
Posted by John Baez
You may be familiar with Raymond Smullyan’s delightful books packed with puzzles and paradoxes. One of them — not my favorite — is called This Book Needs No Title.
Peter May and I are almost done editing a book that’s quite the opposite. It does need a title.
Background Essays Towards Higher Category Theory would be an accurate description, but it’s not very snappy. Towards Higher Category Theory is overly ambitious. Can you think of something better?
To help you dream up an appropriate title, here’s a draft of the preface. And if you spot mistakes in this preface, I’d like to hear about them. (The bibliography makes no pretensions to completeness, so surely many people will be offended by how we have neglected their work. If you’re one of those people, I apologize.)
Cohomology and Homotopy
Posted by David Corfield
In posts and this Lab entry, Urs has been promoting his view of cohomology as about Hom spaces between objects in certain settings, where the unknown space is on the left. Similarly homotopy is where the unknown space is on the right. This got me thinking the following thoughts during some quiet moments in a conference this morning.
June 20, 2009
Hopf Algebras in Luxembourg
Posted by John Baez
Hopf algebras lie at a fascinating intersection of combinatorics, quantum physics, topology and category theory. Everyone should learn about them. Luckily, there is still some funding for students and young researchers to attend this conference and school on Hopf algebras:
- Hopf-in-Lux: School-Conference on Hopf algebras, July 13-17, 2009, University of Luxembourg, organized by Said Benayadi, Philippe Bonneau, Yael Fregier and Martin Schlichenmaier.
This Week’s Finds in Mathematical Physics (Week 276)
Posted by John Baez
In week276 of This Week’s Finds, hear the shocking news about this star:
Read about the Local Bubble, the Loop I Bubble, the cloudlets from Sco-Gen, and the “local fluff”. Come visit the Lab! And learn how Paul-André Mélliès and Nicolas Tabareau have taken some classic results of Lawvere on algebraic theories and generalized them to other kinds of theories, like PROPs.
Kan Lifts
Posted by David Corfield
I’ve been thinking more about organising principles operating in mathematics. I remember Steenrod wrote a very illuminating sketch of algebraic topology in terms of extensions and lifts, which I can’t now retrieve. That got me wondering, if with Mac Lane we say
The notion of Kan extensions subsumes all the other fundamental concepts of category theory,
whatever happened to Kan lifts?
June 16, 2009
Accessible Even to a Philosopher
Posted by David Corfield
Edward Frenkel has a paper out today – Gauge Theory and Langlands Duality – which sets out from André’s Weil’s letter to his sister.
This is a remarkable document, in which Weil tries to explain, in fairly elementary terms (presumably, accessible even to a philosopher), the “big picture” of mathematics, the way he saw it. I think this sets a great example to follow for all of us.
Martin Krieger provided a translation of the letter. As for its accessibility, I can say that it did inspire chapter 4 of my book. Let’s hope Frenkel’s paper can also be inspirational. At first glance, however, it looks tough going.
June 15, 2009
2-Branes in 11 Dimensions
Posted by John Baez
I’m trying to learn a teeny bit more about supersymmetric membrane theories, and I’m so far behind that this old review article is proving helpful:
- Micheal J. Duff, Supermembranes: the first fifteen weeks, Classical and Quantum Gravity 5 (1988), 189–205.
I’m particularly fascinated by the classification of ‘fundamental super -branes’ and its relation to normed division algebras:
- Reals: 2-branes in 4 dimensions, with 1 bosonic and 1 fermionic degree of freedom.
- Complexes: 3-branes in 6 dimensions, with 2 bosonic and 2-fermionic degrees of freedom.
- Quaternions: 5-branes in 10 dimensions, with 4 bosonic and 4 fermionic degrees of freedom.
- Octonions: 2-branes in 11 dimensions, with 8 bosonic and 8 fermionic degrees of freedom.
I talked about this ‘brane scan’ in incredibly elementary terms back in week118, but now I’d like to actually understand it. It’s supposed to follow from something like a classification of closed differential forms on super-Minkowski spacetimes, due to Achúcarro et al. I don’t know how it goes, but it seems potentially quite comprehensible.
If anyone can help me with this, I’d appreciate it a lot. But I really want to say a word about the 11-dimensional case — a brief explanation for complete novices such as myself — and then ask a question about that.
June 14, 2009
This Week’s Finds in Mathematical Physics (Week 275)
Posted by John Baez
In week275 of This Week’s Finds, read about progress towards proving the Cobordism Hypothesis.
June 10, 2009
Final Exams Again
Posted by John Baez
I’m busy grading final exams for my undergraduate number theory class. The class went quite well — perhaps because instead of proving quadratic reciprocity, I spent time teaching them about arithmetic functions, Dirichlet convolution, Möbius inversion and the like… topics which lead to lots of fun puzzles and computations.
Nonetheless, grading finals is always mind-numbing and dispiriting. I’m sure you’ve seen it — perfectly intelligent people grading finals, trading the most mean-spirited and witless of witticisms just to keep from going insane.
In that spirit, let me report three mildly amusing things I’ve seen so far. Don’t get your hopes up — they’re not nearly as funny as the proof of the infinitude of primes that I described last time I taught this class.
Indeed, I’m sure some of you have seen funnier final exams this year. If so, tell us about ‘em!
June 8, 2009
Strings, Fields, Topology in Oberwolfach
Posted by Urs Schreiber
This week’s workshop at MFO is on Strings, Fields, Topology. We started collecting notes and other material at
Oberwolfach Workshop, June 2009 – Strings, Fields Topology .
This includes today
- Christoph Schweigert and Ingo Runkel on [[CFT]] and algebra in modular tensor categories;
- Dan Freed on [[differential cohomology]] of [[string theory]] [[background fields]];
- Kevin Costello on quantum field theory in terms of [[factorization algebras]].
Algebraic Geometry for Category Theorists
Posted by John Baez
James Dolan and I have spent the last year or so talking about algebraic geometry, trying to learn the basics.
Algebraic geometry should be a lot of fun for category theorists — after all, this is the subject made Grothendieck invent topos theory! But alas, introductions to topos theory don’t seem to explain much about algebraic geometry, and introductions to algebraic geometry don’t seem to fully embrace topos theory. It seems that Grothendieck’s revolution never fully caught on. And that’s sort of sad.