Math News July 20th, 2009
Patrick Stein

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

Math News (26 - 50 of about 3086) (xml) (Feedlist)


A trivial generalisation of Cayley’s theoremTerence Tao
(07.10.2014 14:08h)

One of the first basic theorems in group theory is Cayley’s theorem, which links abstract finite groups with concrete finite groups otherwise known as permutation groups . Theorem 1 Cayley’s theorem Let be a group of some finite order . Then is isomorphic to a subgroup of the symmetric group on elements . Furthermore, this subgroup is simply transitive: given two elements of , there is precisely one element of such that . One can therefore think of as a sort of “universal” group that contains up to isomorphism all the possible groups of order . Proof: The group acts ... [Link]

I know I’ve said it before, but…Charles Siegel
(07.10.2014 13:34h)

Rigorous Trivialities will be returning! Not immediately, but it will be. I’m reorganizing a bit, and as I’m going to be contributing to a blog for the general public via the Kavli Foundation, I’m also going to try to revive this blog. Oh, and I’m on twitter now as @SiegelMath, and we’ll see if I’m capable of microblogging. Lots of experiments in communicating math for me over the next year, we’ll see how it goes, hope that some people are still out there and watching, but even if not, I’ll do my best to draw people back.Filed under: Uncategorized [Link]

Speaking Truth to Parallelism at CornellScott
(03.10.2014 20:42h)

This week I was at my alma mater, Cornell, to give a talk at the 50th anniversary celebration of its computer science department. You can watch the streaming video here; my talk runs from roughly 1:17:30 to 1:56 though if you’ve seen other complexity/physics/humor shows by me, this one is pretty similar, except for the riff about Cornell at the beginning . The other two things in that video—a talk by Tom Henzinger about IST Austria, a bold new basic research institute that he leads, closely modeled after the Weizmann Institute in Israel; and a discussion panel about the future ... [Link]

Blissful ignorance and the Kahneman-Tversky paradoxEhud Friedgut
(02.10.2014 18:09h)

Tversky, Kahneman, and Gili Bar-Hillel WikiPedia . Taken by Maya Bar-Hillel at Stanford, summer 1979. The following post was kindly contributed by Ehud Friedgut. During the past week I’ve been reading, and greatly enjoying Daniel Kahneman’s brilliant book “Thinking fast and Slow”. One of the most intriguing passages in the book is the description of an experiment designed by Kahneman and Tversky which exemplifies a judgmental flaw exhibited by many people, which supposedly indicates an irrational, or inconsistent behavior. I will describe their experiment shortly. I still remember the first time I heard of this experiment, it was related to ... [Link]

The “bounded gaps between primes” Polymath project – a retrospectiveTerence Tao
(01.10.2014 13:11h)

The presumably final article arising from the Polymath8 project has now been uploaded to the arXiv as “The “bounded gaps between primes” Polymath project – a retrospective“. This article, submitted to the Newsletter of the European Mathematical Society, consists of personal contributions from ten different participants at varying levels of stage of career, and intensity of participation on their own experiences with the project, and some thoughts as to what lessons to draw for any subsequent Polymath projects. At present, I do not know of any such projects being proposed, but from recent experience I would imagine that some opportunity ... [Link]

The 18th Midrasha Mathematicae. Jerusalem, JANUARY 18-31In And Around Combinatorics
(29.09.2014 21:07h)

The 18th yearly school in mathematics is devoted this year to combinatorics. It will feature lecture series by Irit Dinur, Joel Hass, Peter Keevash, Alexandru Nica, Alexander Postnikov, Wojciech Samotij, and David Streurer and additional activities. As usual grants for local and travel expences are possible. [Link]

I know I’ve said it before, but…Charles Siegel
(28.09.2014 16:04h)

Rigorous Trivialities will be returning! Not immediately, but it will be. I’m reorganizing a bit, and as I’m going to be contributing to a blog for the general public via the Kavli Foundation, I’m also going to try to revive this blog. Oh, and I’m on twitter now as @SiegelMath, and we’ll see if I’m capable of microblogging. Lots of experiments in communicating math for me over the next year, we’ll see how it goes, hope that some people are still out there and watching, but even if not, I’ll do my best to draw people back.Filed under: Uncategorized [Link]

Derived multiplicative functionsTerence Tao
(25.09.2014 09:28h)

Analytic number theory is often concerned with the asymptotic behaviour of various arithmetic functions: functions or from the natural numbers to the real numbers or complex numbers . In this post, we will focus on the purely algebraic properties of these functions, and for reasons that will become clear later, it will be convenient to generalise the notion of an arithmetic function to functions taking values in some abstract commutative ring . In this setting, we can add or multiply two arithmetic functions to obtain further arithmetic functions , and we can also form the Dirichlet convolution by the usual ... [Link]

Microsoft SVCScott
(23.09.2014 18:10h)

By now, the news that Microsoft abruptly closed its Silicon Valley research lab—leaving dozens of stellar computer scientists jobless—has already been all over the theoretical computer science blogosphere: see, e.g., Lance, Luca, Omer Reingold, Michael Mitzenmacher. I never made a real visit to Microsoft SVC only went there once IIRC, for a workshop, while a grad student at Berkeley ; now of course I won’t have the chance. The theoretical computer science community, in the Bay Area and elsewhere, is now mobilizing to offer visiting positions to the “refugees” from Microsoft SVC, until they’re able to find more permanent employment. ... [Link]

The BookSpeaking Truth to Parallelism
(22.09.2014 20:41h)

A few months ago, I signed a contract with MIT Press to publish a new book: an edited anthology of selected posts from this blog, along with all-new updates and commentary. The book’s tentative title open to better suggestions is Speaking Truth to Parallelism: Dispatches from the Frontier of Quantum Computing Theory. The new book should be more broadly accessible than Quantum Computing Since Democritus, although still far from your typical pop-science book. My goal is to have STTP out by next fall, to coincide with Shtetl-Optimized‘s tenth anniversary. If you’ve been a regular reader, then this book is my ... [Link]

Bagchi’s thesisKowalski
(15.09.2014 18:24h)

Despite everything, there is something to be said for the internet. Just a few days ago, I wanted to reference the work of Bagchi, who provided the probabilistic interpretation of Voronin’s Universality Theorem for the Riemann zeta function. However, the original was unpublished, and one of the few papers of Bagchi on this topic pointedly indicated that he had removed most probabilistic considerations why? if it was at the request of a referee, I can only sigh . But fortunately, lo and behold, the original thesis from 1981 can be found in a very decent scan from the Indian Statistical ... [Link]

Mathematical GymnasticsGil Kalai
(15.09.2014 12:15h)

For the long days of ICM 2014 lectures, and long flights to and from Seoul, some mathematical gymnastics is needed. And this is precisely what Omer Angel taught us in his recent visit. Combining gymnastic with a demonstration of parallel transport and deep insights on human physiology! You want to move from this position to this position without simply rotating your hand. Here are two video-demonstrations by some HUJI top people Click on the picture to see the video. The drill is a sequence of five moves and the video skipped the first. Some other mathematical gymnastics is demonstrated in ... [Link]

“For the first time ever…”Media Item from “Haaretz” Today
(15.09.2014 12:15h)

Maryam Mirzakhani received the medal from South Korea’s president Park Geun-hye. Here is an article from today’s Israeli newspaper Haaretz. It is based on this article by the Guardian Thanks, Manor! . See also this post on Laba’s accidental mathematician and John Baez’ Google+ post. The ICM 2014 started today in Seoul. The International congress taking place once every four years is an exciting event, celebrated by thousands of mathematicians in Seoul and many others all over the world. The opening ceremonies came with the announcement of Artur Avila, Manjul Bhargava, Martin Hairer, and Maryam Mirzakhani as 2014 Fields medalist, ... [Link]

Jim Geelen, Bert Gerards, and Geoff Whittle Solved Rota’s Conjecture on MatroidsGil Kalai
(15.09.2014 12:15h)

Gian Carlo Rota Rota’s conjecture I just saw in the Notices of the AMS a paper by Geelen, Gerards, and Whittle where they announce and give a high level description of their recent proof of Rota’s conjecture. The 1970 conjecture asserts that for every finite field, the class of matroids representable over the field can be described by a finite list of forbidden minors. This was proved by William Tutte in 1938 for binary matroids namely those representable over the field of two elements . For binary matroids Tutte found a single forbidden minor. The ternary case was settled by ... [Link]

Media items on David, Amnon, and NathanGil Kalai
(15.09.2014 12:15h)

David Kazhdan, a very famous mathematician from my department with a super-human understanding of mathematics and more is recovering from a terrible bike accident. Here is an article about him from “Maariv.” In Hebrew Amnon Shashua, a computer science professor at the Hebrew University founded Mobileye fifteen years ago. Here is one of many articles about Mobileye. Mobileye helps eliminate car accidents and her sister company Orcam that Amnon also founded develops aids for the visually impaired. Nathan Keller, now at Bar-Ilan University, is a former Ph D student of mine working in probabilistic combinatorics and he has a parallel ... [Link]

Editorial board of “Journal of K-Theory” on strike, demanding Tony Bak hands over the journal to the K-Theory foundation.Scott Morrison
(15.09.2014 03:43h)

Text of the announcement below: Dear Colleagues, We the undersigned announce that, as of today 15 September 2014, we’re starting an indefinite strike. We will decline all papers submitted to us at the Journal of K-Theory. Our demand is that, as promised in 2007-08, Bak’s family company ISOPP hand over the ownership of the journal to the K-Theory Foundation KTF . The handover must be unconditional, free of charge and cover all the back issues. The remaining editors are cordially invited to join us. Yours Sincerely, Paul Balmer, Spencer Bloch, Gunnar Carlsson, Guillermo Cortinas, Eric Friedlander, Max Karoubi, Gennadi Kasparov, ... [Link]

universities should prioritize academicsSteven Pinker’s inflammatory proposal
(11.09.2014 22:14h)

If you haven’t yet, I urge you to read Steven Pinker’s brilliant piece in The New Republic about what’s broken with America’s “elite” colleges and how to fix it. The piece starts out as an evisceration of an earlier New Republic article on the same subject by William Deresiewicz. Pinker agrees with Deresiewicz that something is wrong, but finds Deresiewicz’s diagnosis of what to be lacking. The rest of Pinker’s article sets out his own vision, which involves America’s top universities taking the radical step of focusing on academics, and returning extracurricular activities like sports to their rightful place as ... [Link]

Quasistrict Symmetric Monoidal 2-Categories via Wire DiagramsThe n-Category Café
(10.09.2014 21:43h)

Guest post by Bruce Bartlett I recently put an article on the arXiv: Bruce Bartlett, Quasistrict symmetric monoidal 2-categories via wire diagrams. It’s about Chris Schommer-Pries’s recent strictification result from his updated thesis, that every symmetric monoidal bicategory is equivalent to a quasistrict one. Since symmetric monoidal bicategories can be viewed as the syntax for ‘stable 3-dimensional algebra’, one aim of the paper is to write out this stuff out in a diagrammatic notation, like this: The other aim is to try to strip down the definition of a ‘quasistrict symmetric monoidal bicategory’, emphasizing the central role played by the ... [Link]

Narrow progressions in the primesTerence Tao
(09.09.2014 23:54h)

Tamar Ziegler and I have just uploaded to the arXiv our paper “Narrow progressions in the primes“, submitted to the special issue “Analytic Number Theory” in honor of the 60th birthday of Helmut Maier. The results here are vaguely reminiscent of the recent progress on bounded gaps in the primes, but use different methods. About a decade ago, Ben Green and I showed that the primes contained arbitrarily long arithmetic progressions: given any , one could find a progression with 0}' title='{r>0}' class='latex' /> consisting entirely of primes. In fact we showed the same statement was true if the primes ... [Link]

ICM2014 — Bhargava, Gentry, Sandersgowers
(07.09.2014 14:44h)

On my last day at the ICM I ended up going to fewer talks. As on the previous two days the first plenary lecture was not to be missed — it was Maryam Mirzakhani — so despite my mounting tiredness I set my alarm appropriately. I was a little surprised when I got there by just how empty it was, until eventually I saw that on the screens at the front it said that the lecture was cancelled because of her Fields medallist’s lecture the following Tuesday. I belonged to the small minority that had not noticed this, partly because ... [Link]

Raise a martini glass for Google and Martinis!Scott
(06.09.2014 17:20h)

We’ve already been discussing this in the comments section of my previous post, but a few people emailed me to ask when I’d devote a separate blog post to the news. OK, so for those who haven’t yet heard: this week Google’s Quantum AI Lab announced that it’s teaming up with John Martinis, of the University of California, Santa Barbara, to accelerate the Martinis group‘s already-amazing efforts in superconducting quantum computing. See here for the MIT Tech‘s article, here for Wired‘s, and here for the WSJ‘s. Besides building some of the best if not the best superconducting qubits in the ... [Link]

Ronnie Brown in ParisThe n-Category Café
(06.09.2014 11:47h)

Ronnie Brown has brought to my attention a talk he gave recently at the Workshop Constructive Mathematics and Models of Type Theory, IHP Paris, 02 June 2014 - 06 June 2014. Title: Intuitions for cubical methods in nonabelian algebraic topology Abstract: The talk will start from the 1-dimensional Seifert-van Kampen Theorem for the fundamental group, then groupoid, and so to a use of strict double groupoids for higher versions. These allow for some precise nonabelian calculations of some homotopy types, obtained by a gluing process. Cubical methods are involved because of the ease of writing multiple compositions, leading to “algebraic ... [Link]

Narrow progressions in the primesTerence Tao
(05.09.2014 11:35h)

Tamar Ziegler and I have just uploaded to the arXiv our paper “Narrow progressions in the primes“, submitted to the special issue “Analytic Number Theory” in honor of the 60th birthday of Helmut Maier. The results here are vaguely reminiscent of the recent progress on bounded gaps in the primes, but use different methods. About a decade ago, Ben Green and I showed that the primes contained arbitrarily long arithmetic progressions: given any , one could find a progression with 0}' title='{r>0}' class='latex' /> consisting entirely of primes. In fact we showed the same statement was true if the primes ... [Link]

Large gaps between consecutive prime numbersTerence Tao
(05.09.2014 11:35h)

Kevin Ford, Ben Green, Sergei Konyagin, and myself have just posted to the arXiv our preprint “Large gaps between consecutive prime numbers“. This paper concerns the “opposite” problem to that considered by the recently concluded Polymath8 project, which was concerned with very small values of the prime gap . Here, we wish to consider the largest prime gap that one can find in the interval as goes to infinity. Finding lower bounds on is more or less equivalent to locating long strings of consecutive composite numbers that are not too large compared to the length of the string. A classic ... [Link]

Matilde Lalin Attending conferences with small childrenmlalin
(05.09.2014 11:35h)

[This guest post is authored by Matilde Lalin, an Associate Professor in the Département de mathématiques et de statistique at the Université de Montréal. I have lightly edited the text, mostly by adding some HTML formatting. -T.] Mathematicians and likely other academics! with small children face some unique challenges when traveling to conferences and workshops. The goal of this post is to reflect on these, and to start a constructive discussion what institutions and event organizers could do to improve the experiences of such participants. The first necessary step is to recognize that different families have different needs. While it ... [Link]

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