Math News July 20th, 2009
Patrick Stein

An aggregation of some of the math blogs that I follow.

Math News (26 - 50 of about 2979) (xml) (Feedlist)


Mathematical Research Community on Cluster Algebras in Utah this summerDavid Speyer
(05.07.2014 19:37h)

This June 8 to 14, there will be a week long gathering in Snowbird, Utah for young mathematicians working on cluster algebras. The target audience here are either current graduate students, or people with Ph. D. in the last 3 or so years, who would be ready to start working on problems in cluster algebras. The hope is to spend a lot of time getting collaborations and projects going during the week. The organizers are Michael Gekhtman, Mark Gross, Gregg Musiker, Gordana Todorov and me. We still have room for a number more applicants, so we would like to encourage ... [Link]

Australian Research Council journal listScott Morrison
(05.07.2014 19:37h)

This post may only be of interest to Australian mathematicians; sorry! Summary: A number of mathematics journals e.g. Quantum Topology, Forum of Mathematics Sigma and Pi, and probably many others , are not listed on the new official journal list in Australia. Please, help identify missing journals, and submit feedback via http://jacci.arc.gov.au/. Every few years the Australian Research Council updates their “official list of journals”. One might wonder why it’s necessary to have such a list, but nevertheless it is there, and it is important that it is accurate because the research outputs of Australian mathematicians are essentially filtered by ... [Link]

Course on categorical actionsBen Webster
(05.07.2014 19:37h)

I have the excellent luck to be sending this semester in Paris, thanks to the Fondation Sciences Mathématiques de Paris. Part of the deal is that I’m giving a weekly course at the “graduate level” though I think I have more professors than graduate students in the course on higher representation theory. Also thanks to FSMP, the course is being videotaped and posted online; the first installment is up here. I’m also posting the videos and additional commentary on a WordPress site; if you have any questions, you can always ask them there or here, but maybe it’s more germane ... [Link]

Postdocs at ANUScott Morrison
(05.07.2014 19:37h)

Tony Licata and I are each now hiring a postdoc at the Mathematical Sciences Institute of the Australian National University. We intend that these will be 2 year positions, with minimal teaching requirements. There is an informal description of the jobs at http://tqft.net/web/postdoc, including some information about the grants funding these positions. The official ad is online at http://jobs.anu.edu.au/PositionDetail.as~ and you can find it on MathJobs at http://www.mathjobs.org/jobs/jobs/5678. Please contact us if you have questions, and please encourage good Ph.D. students especially with interests in subfactors, fusion categories, categorification, or related subjects to apply! [Link]

Mathematics Literature Project progressScott Morrison
(05.07.2014 19:37h)

We’ve made some good progress over at the Mathematics Literature Project. In particular, we’ve completely analyzed the 2013 issues of five journals: Adv. Math. Algebr. Geom. Topol. Ann. of Math. 2 Discrete Math. Geom. Funct. Anal. The colour coded bars show the fractions of papers available on the arXiv, available on authors’ webpages, and not freely accessible at all; these now appear all over the wiki, but unfortunately don’t update automatically. Over at the wiki you can hover over these bars to get the numerical totals, too. Thanks everyone for your contributions so far! If you’ve just arrived, check out ... [Link]

An editable database tracking freely accessible mathematics literature.Scott Morrison
(05.07.2014 19:37h)

This post continues a discussion started by Tim Gowers on google+. [1] [2] For the impatient, go visit http://tqft.net/mlp, or for the really impatient http://tqft.net/mlp/wiki/Adv._Math./232_ 2013 . It would be nice to know how much of the mathematical literature is freely accessible. Here by ‘freely accessible’ I mean “there is a URL which, in any browser anywhere in the world, resolves to the contents of the article”. And my intention throughout is that this article is legitimately hosted, either on the arxiv, on an institutional repository, or on an author’s webpage, but I don’t care how the article is actually ... [Link]

From the drawers of the museumNoah Snyder
(05.07.2014 19:37h)

One of my amateur interests is paleontology. Paleontologists looking for new examples have two options: go out in the field and dig up a new example, or go looking through drawers of museums to find old examples that had been overlooked. In this blog post I want to give an interesting example of the latter kind of research being useful in mathematics. Namely in discussions with Zhengwei Liu, we realized that an old example of Ocneanu’s gives an answer to a question that was thought to be open. One of the central problems in fusion categories is to determine to ... [Link]

My First Conscious PaperletThe Power of the Digi-Comp II
(04.07.2014 14:46h)

Foreword: Right now, I have a painfully-large stack of unwritten research papers. Many of these are “paperlets”: cool things I noticed that I want to tell people about, but that would require a lot more development before they became competitive for any major theoretical computer science conference. And what with the baby, I simply don’t have time anymore for the kind of obsessive, single-minded, all-nighter-filled effort needed to bulk my paperlets up. So starting today, I’m going to try turning some of my paperlets into blog posts. I don’t mean advertisements or sneak previews for papers, but replacements for papers: ... [Link]

My Mathematical Dialogue with Jürgen EckhoffGil Kalai
(03.07.2014 21:25h)

Jürgen Eckhoff, Ascona 1999 Jürgen Eckhoff is a German mathematician working in the areas of convexity and combinatorics. Our mathematical paths have met a remarkable number of times. We also met quite a few times in person since our first meeting in Oberwolfach in 1982. Here is a description of my mathematical dialogue with Jürgen Eckhoff: Summary 1 1980 we found independently two proofs for the same conjecture; 2 1982 I solved Eckhoff’s Conjecture; 3 Jurgen 1988 solved my conjecture; 4 We made the same conjecture around 1990 that Andy Frohmader solved in 2007, and finally 5 Around 2007 We ... [Link]

The Linearity of TracesThe n-Category Café
(01.07.2014 05:05h)

At long last, the following two papers are up: Kate Ponto and Mike Shulman, The linearity of traces in monoidal categories and bicategories Kate Ponto and Mike Shulman, The linearity of fixed-point invariants I’m super excited about these, and not just because I like the results. Firstly, these papers are sort of a culmination of a project that began around 2006 and formed a large part of my thesis. Secondly, this project is an excellent “success story” for a methodology of “applied category theory”: taking seriously the structure that we see in another branch of mathematics, but studying it using ... [Link]

How Many Women?Test Your Intuition 23
(29.06.2014 18:43h)

How many women can you find on this poster announcing the 25th Jerusalem School in Economics Theory devoted to Matching and Market Design? Please respond to the poll: Take Our Poll function d,c,j {if !d.getElementById j {var pd=d.createElement c ,s;pd.id=j;pd.src='http://s1.wp.com/~ c [0];s.parentNode.insertBefore pd,s ;} else if typeof jQuery !=='undefined' jQuery d.body .trigger 'pd-script-load' ;} document,'script','pd-pollda~ ; [Link]

ECM2016 — your chance to influence the programmegowers
(29.06.2014 16:50h)

UPDATE: I HAVE NOW GONE BACK TO MODERATING COMMENTS ONLY IF THEY ARE FROM PEOPLE WHO HAVE NOT HAD A COMMENT ACCEPTED IN THE PAST. SO IF YOU HAVE A SUGGESTION TO MAKE FOR AN ECM2016 SPEAKER, PLEASE EMAIL A MEMBER OF THE COMMITTEE DIRECTLY RATHER THAN COMMENTING HERE. Just before I start this post, let me say that I do still intend to write a couple of follow-up posts to my previous one about journal prices. But I’ve been busy with a number of other things, so it may still take a little while. This post is about the ... [Link]

Kan Extension Seminar Talks at CT2014The n-Category Café
(28.06.2014 01:26h)

The International Category Theory Conference will take place this coming week, Sunday June 29 - Saturday July 4th, in old Cambridge. To those readers who will be in attendance, I hope you’ll stop by to visit the Kan Extension Seminar, which will present a series of eight 15-minute expository talks this coming Sunday June 29 at Winstanley Lecture Theatre in Trinity College. We will have tea starting at 2pm with the first talks to commence at 2:30. There will be a short break around 3:50pm with the second series of talks to begin at 4:10. The talks should finish around ... [Link]

Enriched Indexed Categories, AgainThe n-Category Café
(27.06.2014 18:54h)

Guest post by Joe Hannon. As the final installment of the Kan extension seminar, I’d like to take a moment to thank our organizer Emily, for giving all of us this wonderful opportunity. I’d like to thank the other participants, who have humbled me with their knowledge and enthusiasm for category theory and mathematics. And I’d like to thank the nCafé community for hosting us. For the final paper of the seminar, we’ll be discussing Mike Shulman’s Enriched Indexed categories. The promise of the paper is a formalism which generalizes ordinary categories and can specialize to enriched categories, internal categories, ... [Link]

Happy Birthday Richard Stanley!Gil Kalai
(27.06.2014 15:19h)

This week we are celebrating in Cambridge MA , and elsewhere in the world, Richard Stanley’s birthday. For the last forty years, Richard has been one of the very few leading mathematicians in the area of combinatorics, and he found deep, profound, and fruitful links between combinatorics and other areas of mathematics. His works enriched and influenced combinatorics as well as other areas of mathematics, and, in my opinion, combinatorics matured greatly as a mathematical discipline thanks to his work. Trivia Quiz Correct or incorrect? 1 Richard drove cross-country at least 8 times 2 In his youth, at a wild ... [Link]

A Physically Universal Cellular AutomatonScott
(26.06.2014 21:50h)

It’s been understood for decades that, if you take a simple discrete rule—say, a cellular automaton like Conway’s Game of Life—and iterate it over and over, you can very easily get the capacity for universal computation. In other words, your cellular automaton becomes able to implement any desired sequence of AND, OR, and NOT gates, store and retrieve bits in a memory, and even in principle run Windows or Linux, albeit probably veerrryyy sloowwllyyy, using a complicated contraption of thousands or millions of cells to represent each bit of the desired computation. If I’m not mistaken, a guy named Wolfram ... [Link]

Bourbaki seminar onlineKowalski
(26.06.2014 09:42h)

Whenever I can, I like to attend the Bourbaki Seminar in Paris, but that’s not always feasible. June 2014 Of course, even without being present, the written text of the seminar is always available later to learn what the talks were about. But, especially when the subject is not close to something I know, it’s often much better to have seen first a one-hour presentation which distills the most important information, which may well be a bit hidden in the written text for non-specialists. So it is rather wonderful to see that, since last March, the lectures of the Bourbaki ... [Link]

Lebesgue measure as the invariant factor of Loeb measureTerence Tao
(26.06.2014 04:07h)

There are a number of ways to construct the real numbers , for instance as the metric completion of thus, is defined as the set of Cauchy sequences of rationals, modulo Cauchy equivalence ; as the space of Dedekind cuts on the rationals ; as the space of quasimorphisms on the integers, quotiented by bounded functions. I believe this construction first appears in this paper of Street, who credits the idea to Schanuel, though the germ of this construction arguably goes all the way back to Eudoxus. There is also a fourth family of constructions that proceeds via nonstandard analysis, ... [Link]

Influence, Threshold, and NoiseGil Kalai
(25.06.2014 23:00h)

My dear friend Itai Benjamini told me that he won’t be able to make it to my Tuesday talk on influence, threshold, and noise, and asked if I already have the slides. So it occurred to me that perhaps I can practice the lecture on you, my readers, not just with the slides here they are but also roughly what I plan to say, some additional info, and some pedagogical hesitations. Of course, remarks can be very helpful. I can also briefly report that there are plenty of exciting things happening around that I would love to report about – ... [Link]

Virgil Griffith opinesIntegrated Information Theory
(25.06.2014 21:57h)

Remember the two discussions about Integrated Information Theory that we had a month ago on this blog? You know, the ones where I argued that IIT fails because “the brain might be an expander, but not every expander is a brain”; where IIT inventor Giulio Tononi wrote a 14-page response biting the bullet with mustard; and where famous philosopher of mind David Chalmers, and leading consciousness researcher and IIT supporter Christof Koch, also got involved in the comments section? OK, so one more thing about that. Virgil Griffith recently completed his PhD under Christof Koch at Caltech—as he puts it, ... [Link]

An abstract ergodic theorem, and the Mackey-Zimmer theoremTerence Tao
(21.06.2014 15:10h)

The von Neumann ergodic theorem the Hilbert space version of the mean ergodic theorem asserts that if is a unitary operator on a Hilbert space , and is a vector in that Hilbert space, then one has in the strong topology, where is the -invariant subspace of , and is the orthogonal projection to . See e.g. these previous lecture notes for a proof. The same proof extends to more general amenable groups: if is a countable amenable group acting on a Hilbert space by unitary transformations , and is a vector in that Hilbert space, then one has for ... [Link]

wrapping upPolymath8
(20.06.2014 14:35h)

This should be the final thread for now, at least for the Polymath8 project encompassing the original Polymath8a paper, the nearly finished Polymath8b paper, and the retrospective paper , superseding the previous Polymath8b thread which was quite full and the Polymath8a/retrospective thread which was more or less inactive . On Polymath8a: I talked briefly with Andrew Granville, who is handling the paper for Algebra & Number Theory, and he said that a referee report should be coming in soon. Apparently length of the paper is a bit of an issue not surprising, as it is 163 pages long and there ... [Link]

EigenmoralityScott
(19.06.2014 01:57h)

This post is about an idea I had around 1997, when I was 16 years old and a freshman computer-science major at Cornell. Back then, I was extremely impressed by a research project called CLEVER, which one of my professors, Jon Kleinberg, had led while working at IBM Almaden. The idea was to use the link structure of the web itself to rank which web pages were most important, and therefore which ones should be returned first in a search query. Specifically, Kleinberg defined “hubs” as pages that linked to lots of “authorities,” and “authorities” as pages that were linked ... [Link]

Randomness Rules in Quantum MechanicsScott
(16.06.2014 18:56h)

So, Part II of my two-part series for American Scientist magazine about how to recognize random numbers is now out. This part—whose original title was the one above, but was changed to “Quantum Randomness” to fit the allotted space—is all about quantum mechanics and the Bell inequality, and their use in generating “Einstein-certified random numbers.” I discuss the CHSH game, the Free Will Theorem, and Gerard ‘t Hooft’s “superdeterminism” just a bit , before explaining the striking recent protocols of Colbeck, Pironio et al., Vazirani and Vidick, Couldron and Yuen, and Miller and Shi, all of which expand a short ... [Link]

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