Math News July 20th, 2009
Patrick Stein

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

Math News (26 - 50 of about 3027) (xml) (Feedlist)

ICM2014 — introductory postgowers
(11.08.2014 23:44h)

Four years ago I blogged from the ICM in Hyderabad. The posts are amongst the most popular I have written — my statistics show that some of them are still being read quite regularly even now. Right now I’m sitting in Charles de Gaulle airport waiting to board a plane to Seoul, where I will be attending this year’s ICM, or rather, as I did last time, attending the first half of it. I’m not sure I’ll have the time or energy to write quite as much about ICM2014 as I did about ICM2010, but I’ll do what I can. ... [Link]

Impressions de la rechercheKowalski
(10.08.2014 10:46h)

Although my knowledge of French literature is rather shamefully fragmentary, I’ve at least, this year, managed to close one gap: I read À la recherche du temps perdu between January and last week-end. This was where I found a very funny allusion to esoteric monographs it’s in the second book, À l’ombre des jeunes filles en fleurs . Did I like the book? This is probably far from the right question to ask in any case, but it’s therefore worth investigating in a post-modern spirit. Since I finished the whole of the seven volumes in about seven months, during which ... [Link]

Jim Geelen, Bert Gerards, and Geoï¬Gil Kalai
(08.08.2014 05:40h)

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]

The Ten-Fold Way Part 3 The n-Category Café
(07.08.2014 05:00h)

My last article on the ten-fold way was a piece of research in progress — it only reached a nice final form in the comments. Since that made it rather hard to follow, let me try to present a more detailed and self-contained treatment here! But if you’re in a hurry, you can click on this: and get my poster for next week’s scientific advisory board meeting at the Centre for Quantum Technologies, in Singapore. That’s where I work in the summer, and this poster is supposed to be a terse introduction to the ten-fold way. First we’ll introduce the ... [Link]

Media items on David, Amnon, and NathanGil Kalai
(06.08.2014 02:16h)

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]

(05.08.2014 07:41h)

As pointed out by Philippe, this abstruse goose cartoon shows that analytic number theory is now part of the Zeitgeist. [Link]

Variants of the Selberg sieve, and bounded intervals containing many primesTerence Tao
(03.08.2014 21:34h)

I’ve just uploaded to the arXiv the D.H.J. Polymath paper “Variants of the Selberg sieve, and bounded intervals containing many primes“, which is the second paper to be produced from the Polymath8 project the first one being discussed here . We’ll refer to this latter paper here as the Polymath8b paper, and the former as the Polymath8a paper. As with Polymath8a, the Polymath8b paper is concerned with the smallest asymptotic prime gap where denotes the prime, as well as the more general quantities In the breakthrough paper of Goldston, Pintz, and Yildirim, the bound was obtained under the strong hypothesis ... [Link]

The parity problem obstruction for the binary Goldbach problem with bounded errorTerence Tao
(03.08.2014 21:34h)

Two of the most famous open problems in additive prime number theory are the twin prime conjecture and the binary Goldbach conjecture. They have quite similar forms: Twin prime conjecture The equation has infinitely many solutions with prime. Binary Goldbach conjecture The equation has at least one solution with prime for any given even . In view of this similarity, it is not surprising that the partial progress on these two conjectures have tracked each other fairly closely; the twin prime conjecture is generally considered slightly easier than the binary Goldbach conjecture, but broadly speaking any progress made on one ... [Link]

Hilbert’s fifth problem and approximate groupsTerence Tao
(03.08.2014 21:34h)

Due to some requests, I’m uploading to my blog the slides for my recent talk in Segovia for the birthday conference of Michael Cowling on “Hilbert’s fifth problem and approximate groups“. The slides cover essentially the same range of topics in this series of lecture notes, or in this text of mine, though of course in considerably less detail, given that the slides are meant to be presented in an hour.Filed under: math.CA, math.GR, talk [Link]

Lebesgue measure as the invariant factor of Loeb measureTerence Tao
(03.08.2014 21:34h)

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]

An abstract ergodic theorem, and the Mackey-Zimmer theoremTerence Tao
(03.08.2014 21:34h)

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
(03.08.2014 21:34h)

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]

When is correlation transitive?Terence Tao
(03.08.2014 21:34h)

Given two unit vectors in a real inner product space, one can define the correlation between these vectors to be their inner product , or in more geometric terms, the cosine of the angle subtended by and . By the Cauchy-Schwarz inequality, this is a quantity between and , with the extreme positive correlation occurring when are identical, the extreme negative correlation occurring when are diametrically opposite, and the zero correlation occurring when are orthogonal. This notion is closely related to the notion of correlation between two non-constant square-integrable real-valued random variables , which is the same as the correlation ... [Link]

Wrestling with Tight SpansThe n-Category Café
(02.08.2014 04:31h)

I’ve been spending some time with Simon Willerton’s paper Tight spans, Isbell completions and semi-tropical modules. In particular, I’ve been trying to understand tight spans. The tight span of a metric space AA is another metric space T A T A , in which AA naturally embeds. For instance, the tight span of a two-point space is a line segment containing the original two points as its endpoints. Similarly, the tight span of a three-point space is a space shaped like the letter Y, with the original three points at its tips. Because of examples like this, some people like ... [Link]

<i>Basic Category Theory</i>The n-Category Café
(27.07.2014 21:42h)

My new book is out! Click the image for more information. It’s an introductory category theory text, and I can prove it exists: there’s a copy right in front of me. You too can purchase a proof. Is it unique? Maybe. Here are three of its properties: It doesn’t assume much. It sticks to the basics. It’s short. I want to thank the nn-Café patrons who gave me encouragement during my last week of work on this. As I remarked back then, some aspects of writing a book — even a short one — require a lot of persistence. But ... [Link]

The Ten-Fold Way Part 2 The n-Category Café
(27.07.2014 13:06h)

How can we discuss all the kinds of matter described by the ten-fold way in a single setup? It’s bit tough, because 8 of them are fundamentally ‘real’ while the other 2 are fundamentally ‘complex’. Yet they should fit into a single framework, because there are 10 super division algebras over the real numbers, and each kind of matter is described using a super vector space — or really a super Hilbert space — with one of these super division algebras as its ‘ground field’. Combining physical systems is done by tensoring their Hilbert spaces… and there does seem to ... [Link]

Let in cryptographers and other scientistsUS State Department
(26.07.2014 19:31h)

Predictably, my last post attracted plenty of outrage some of it too vile to let through , along with the odd commenter who actually agreed with what I consider my fairly middle-of-the-road, liberal Zionist stance. But since the outrage came from both sides of the issue, and the two sides were outraged about the opposite things, I guess I should feel OK about it. Still, it’s hard not to smart from the burns of vituperation, so today I’d like to blog about a very different political issue: one where hopefully almost all Shtetl-Optimized readers will actually agree with me ! ... [Link]

IHÉS summer school onlineKowalski
(26.07.2014 15:52h)

The IHÉS Summer School on analytic number theory that I co-organized with Philippe Michel ended a few days ago. Even if the weather did not cooperate rain, scorching heat, gloomy clouds , I think it went very well, although this is of course more for the participants to say… I certainly learnt things myself, especially in the course of K. Soundararajan, who discussed among other things some recent works of his with M. Radziwiƚƚ that I had intended to read, without finding the time… My own lectures were on trace functions over finite fields. It was the first occasion I’ve ... [Link]

3-sentence summary of what’s happening in Israel and GazaScott
(24.07.2014 13:34h)

Hamas is trying to kill as many civilians as it can. Israel is trying to kill as few civilians as it can. Neither is succeeding very well. Update July 28 : Please check out a superb essay by Sam Harris on the Israeli/Palestinian conflict. While, as Harris says, the essay contains “something to offend everyone”—even me—it also brilliantly articulates many of the points I’ve been trying to make in this comment thread. See also a good HuffPost article by Ali A. Rizvi, a “Pakistani-Canadian writer, physician, and musician.” [Link]

Special Day on Quantum PCP, Quantum Codes, Simplicial Complexes and Locally Testable CodesNext Week in Jerusalem
(24.07.2014 00:56h)

Special Quantum PCP and/or Quantum Codes: Simplicial Complexes and Locally Testable CodesDay בי”ס להנדסה ולמדעי המחשב 24 Jul 2014 - 09:30 to 17:00 room B-220, 2nd floor, Rothberg B Building On Thursday, the 24th of July we will host a SC-LTC simplicial complexes and classical and quantum locally testable codes at the Hebrew university, Rothberg building B room 202 second floor in the Givat Ram campus. Please join us, we are hoping for a fruitful and enjoyable day, with lots of interactions. Coffee and refreshments will be provided throughout the day, as well as free “tickets” for lunch on campus ... [Link]

The human factorIzabella Laba
(23.07.2014 03:49h)

A recent Telegraph article suggests that “females, as a whole, are not hugely engaged by science.” Emphasis mine: The problem with science is that, for all its wonders, it lacks narrative and story-line. Science and maths is about facts, and the laboratory testing of elements. It is not primarily about people. Women – broadly speaking – are drawn to the human factor: to story, biography, psychology and language. This self-proclaimed people specialist keeps referring to women as “females,” the noun more often than the adjective. For instance: “Biology and nature, he suggested, will generally nudge females away from [science and ... [Link]

“How Might Quantum Information Transform Our Future?”Scott
(22.07.2014 13:57h)

So, the Templeton Foundation invited me to write a 1500-word essay on the above question. It’s like a blog post, except they pay me to do it! My essay is now live, here. I hope you enjoy my attempt at techno-futurist prose. You can comment on the essay either here or over at Templeton’s site. Thanks very much to Ansley Roan for commissioning the piece. [Link]

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