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

Math News (1 - 25 of about 3158) (xml) (Feedlist)

## Worms, brains and “graphes expanseurs”Kowalski

(11.04.2015 11:03h)

Two days ago, I was in Paris and visited the École Polytechnique there for the first time, as it turns out , in order to give the traditional introductory lecture presenting various aspects of mathematics that is given each year to the incoming class of students. Many people would wonder how a new class can be incoming in April; this is because the students of École Polytechnique, which is a military school, begin their studies with a military/civil service from September to April . I had selected expander graphs as the topic of my talk, as being simultaneously a very ... [Link]

## Kummer extensions, Hilbert’s Theorem 90 and judicious expansionKowalski

(26.03.2015 15:45h)

This semester, I am teaching “Algebra II” for the first time. After “Algebra I” which covers standard “Groups, rings and fields”, this follow-up is largely Galois theory. In particular, I have to classify cyclic extensions. In the simplest case where is a cyclic extension of degree and contains all -th roots of unity and is coprime to the characteristic of , this essentially means proving that if has cyclic Galois group of order , then there is some with and belongs to . Indeed, the converse is relatively simple in the technical sense that I can do it on paper ... [Link]

## Noether on GoogleKowalski

(23.03.2015 09:35h)

Today’s Google doodle celebrates Emmy Noether. Noether Algebra would look very different without her “successive sets of symbols with the same second suffix“ . [Link]

## A parity lemma of A. IrvingKowalski

(16.03.2015 10:31h)

In his recent work on the divisor function in arithmetic progressions to smooth moduli, A. Irving proves the following rather amusing lemma see Lemma 4.5 in his paper : Lemma Let be an odd prime number, let be an integer and let be a -tuple of elements of . For any subset of , denote and for any , let denote the multiplicity of among the . Then if none of the is zero, there exists some for which is odd. I will explain two proofs of this result, first Irving’s, and then one that I came up with. I’m ... [Link]

## Who proved the Peter-Weyl theorem for compact groups?Kowalski

(15.03.2015 18:03h)

Tamas Hausel just asked me because of my previous post on the paper of Peter and Weyl how could Peter and Weyl have proved the “Peter-Weyl Theorem” for compact groups in 1926, not having Haar measure at their disposal? Indeed, Haar’s work is from 1933! The answer is easy to find, although I had completely overlooked the point when reading the paper: Peter and Weyl assume that their compact group is a compact Lie group, which allows them to discuss Haar measure using differential forms! Peter-Weyl So the question is: who first proved the full “Peter-Weyl” Theorem for all compact ... [Link]

## The ultimate physical limits of privacyScott

(11.03.2015 15:44h)

Somewhat along the lines of my last post, the other day a reader sent me an amusing list of questions about privacy and fundamental physics. The questions, and my answers, are below. 1. Does the universe provide us with a minimum level of information security? I’m not sure what the question means. Yes, there are various types of information security that are rooted in the known laws of physics—some of them like quantum key distribution even relying on specific aspects of quantum physics—whose security one can argue for by appealing to the known properties of the physical world. Crucially, however, ... [Link]

## The flow of emails within the block inboxScott

(07.03.2015 16:06h)

As a diversion from the important topics of shaming, anti-shaming, and anti-anti-shaming, I thought I’d share a little email exchange with my interlocutor’s kind permission , which gives a good example of what I find myself doing all day when I’m not blogging, changing diapers, or thinking about possibly doing some real work but where did all the time go? . Dear Professor Aaronson, I would be very pleased to know your opinion about time. In a letter of condolence to the Besso family, Albert Einstein wrote: “Now he has departed from this strange world a little ahead of me. ... [Link]

## RadioKowalski

(27.02.2015 17:31h)

For those readers who understand spoken French or simply appreciate the musicality of the language and are interested in the history of mathematics, I warmly recommend listening to the recording of a recent programme of Radio France Internationale entitled “Pourquoi Bourbaki ?” In addition to the dialogue of Sophie Joubert with Michèle Audin and Antoine Chambert-Loir, one can hear some extracts of older émissions with L. Schwartz, A. Weil, H. Cartan, J. Dieudonné, for instance. [Link]

## How can we fight online shaming campaigns?Scott

(25.02.2015 13:15h)

Longtime friend and colleague Boaz Barak sent me a fascinating New York Times Magazine article that profiles people who lost their jobs or otherwise had their lives ruined, because of a single remark that then got amplified a trillionfold in importance by social media. The author, Jon Ronson, also has a forthcoming book on the topic. The article opens with Justine Sacco: a woman who, about to board a flight to Cape Town, tweeted “Going to Africa. Hope I don’t get AIDS. Just kidding. I’m white!” To the few friends who read Sacco’s Twitter feed, it would’ve been obvious that ... [Link]

## “The Man Who Tried to Redeem the World with Logic”Scott

(18.02.2015 17:21h)

No, I’m not talking about me! Check out an amazing Nautilus article of that title by Amanda Gefter, a fine science writer of my acquaintance. The article tells the story of Walter Pitts, who [spoiler alert] grew up on the mean streets of Prohibition-era Detroit, discovered Russell and Whitehead’s Principia Mathematica in the library at age 12 while hiding from bullies, corresponded with Russell about errors he’d found in the Principia, then ran away from home at age 15, co-invented neural networks with Warren McCulloch in 1943, became the protégé of Norbert Wiener at MIT, was disowned by Wiener because ... [Link]

## MemrefutingScott

(11.02.2015 21:47h)

in which I bring this blog back to the “safe, uncontroversial” territory of arguing with people who think they can solve NP-complete problems in polynomial time A few people have asked my opinion about “memcomputing”: a computing paradigm that’s being advertised, by its developers, as a way to solve NP-complete problems in polynomial time. According to the paper Memcomputing NP-complete problems in polynomial time using polynomial resources and collective states, memcomputing “is based on the brain-like notion that one can process and store information within the same units memprocessors by means of their mutual interactions.” The authors are explicit that, ... [Link]

## Аналитическая теория чиселKowalski

(09.02.2015 19:06h)

Thanks to the recent Russian translation of my book with Henryk Iwaniec, I can now at least read my own last name in Cyrillic; I wonder what the two extra letters really mean… Analytic Number Theory in Russian [Link]

## Read the Fine PrintQuantum Machine Learning Algorithms

(02.02.2015 17:01h)

So, I’ve written a 4-page essay of that title, which examines the recent spate of quantum algorithms for clustering, classification, support vector machines, and other “Big Data” problems that grew out of a 2008 breakthrough on solving linear systems by Harrow, Hassidim, and Lloyd, as well as the challenges in applying these algorithms to get genuine exponential speedups over the best classical algorithms. An edited version of the essay will be published as a Commentary in Nature Physics. Thanks so much to Iulia Georgescu at Nature for suggesting that I write this. Update April 4, 2015 : The piece has ... [Link]

## An ideal hypothetical listKowalski

(29.01.2015 14:00h)

A few months ago, for purposes that will remain clouded in mystery for the moment, I had the occasion to compose an ideal list of rare books of various kinds, which do not necessarily exist. Here is what I came up with: i “The Elements of the Most Noble game of Whist; elucidated and discussed in all details”, by A. Bandersnatch, Duke Dimitri, N. Fujisaki, A. Grothendieck, Y. Grünfiddler, J. Hardy, Jr., B. Kilpatrick and an Anonymous Person. ii “Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom funften Grade”, by F. Klein; with barely legible annotations and initialed ... [Link]

## More conferencesKowalski

(29.01.2015 13:56h)

It seems that most of my posts these days are devoted to announcing conferences in which I am involved as organizer… Indeed, there are two coming up this year actually three, if I count the MSRI summer school : 1 May 14 and 15, we will have the Number Theory Days 2015 at EPF Lausanne; the speakers are Gaetan Chenevier, Henryk Iwaniec, Alena Pirutka, Chris Skinner and Zhiwei Yun; this is co-organized by Ph. Michel and myself. 2 Immediately afterward, from May 18 to 22, comes a conference at FIM, co-organized by H. Iwaniec, Ph. Michel and myself, with the ... [Link]

## Happy Second Birthday LilyScott

(21.01.2015 22:07h)

Two years ago, I blogged when Lily was born. Today I can blog that she runs, climbs, swims sort of , constructs 3-word sentences, demands chocolate cake, counts to 10 in both English and Hebrew, and knows colors, letters, shapes, animals, friends, relatives, the sun, and the moon. To all external appearances she’s now conscious as you and I are and considerably more so than the cat in the photo . But the most impressive thing Lily does—the thing that puts her far beyond where her parents were at the same age, in a few areas—is her use of the ... [Link]

## BQP/LHC collisionScott

(15.01.2015 21:25h)

This afternoon, I gave my usual spiel about Quantum Computing and the Limits of the Efficiently Computable at the CERN Colloquium. If you watched the webcast of the Higgs boson discovery announcement a couple years ago, it was in the same auditorium they used for that, except this time it was less packed. Beforehand, Dana and I got to join a tour of the CMS detector at the Large Hadron Collider—one of the very last tours, before CMS shuts down as ATLAS already has to get ready for collisions at the LHC’s new, higher energy. Considered as eye candy, I’d ... [Link]

## Quantum computing news items by reader request Scott

(12.01.2015 17:41h)

Within the last couple months, there was a major milestone in the quest to build a scalable quantum computer, and also a major milestone in the quest to figure out what you would do with a quantum computer if you had one. As I’ve admitted many times, neither of those two quests is really the reason why I got into quantum computing—I’m one of the people who would still want to study this field, even if there were no serious prospect either of building a quantum computer or of doing anything useful with it for a thousand years—but for some ... [Link]

## Fenchel-Nielsen CoordinatesCharles Siegel

(06.01.2015 07:00h)

Welcome back, and hope all you readers had a good 2014 and particularly good holidays and new year’s celebrations, if you do those things. Today, we’re going to keep on the road to producing the moduli space of curves, by nailing down some more hyperbolic geometry. Secretly knowing the answer to what the dimension of the moduli space is over the reals, it’s , I know how many coordinates we need to construct. Half of them come immediately from the discussion last time of pairs of pants: Theorem: For any triple of positive numbers , there exists a unique, up ... [Link]

## Probabilistic models and heuristics for the primes optional 254A, Supplement 4

(05.01.2015 07:36h)

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## What I believeScott

(30.12.2014 16:30h)

Two weeks ago, prompted by a commenter named Amy, I wrote by far the most personal thing I’ve ever made public—what’s now being referred to in some places as just “comment 171.” My thinking was: I’m giving up a privacy that I won’t regain for as long as I live, opening myself to ridicule, doing the blog equivalent of a queen-and-two-rook sacrifice. But at least—and this is what matters—no one will ever again be able to question the depth of my feminist ideals. Not after they understand how I clung to those ideals through a decade when I wanted to ... [Link]

## Quantum Complexity Theory Student Project Showcase 3Scott

(26.12.2014 06:33h)

Merry Christmas belatedly ! This year Quanta Claus has brought us eight fascinating final project reports from students in my 6.845 Quantum Complexity Theory class, covering everything from interactive proofs to query and communication complexity to quantum algorithms to quantum gates and one project even includes a web-based demo you can try! . Continuing in the tradition of the two previous showcases, I’m sharing the reports here; some of these works might also be posted to the arXiv and/or submitted to journals. Thanks so much to the students who volunteered to participate in the showcase, and to all the students ... [Link]

## The Erdos-Ulam problem, varieties of general type, and the Bombieri-Lang conjectureTerence Tao

(26.12.2014 04:50h)

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## Long gaps between primesTerence Tao

(26.12.2014 04:50h)

Kevin Ford, Ben Green, Sergei Konyagin, James Maynard, and I have just uploaded to the arXiv our paper “Long gaps between primes“. This is a followup work to our two previous papers discussed in this previous post , in which we had simultaneously shown that the maximal gap between primes up to exhibited a lower bound of the shape for some function that went to infinity as ; this improved upon previous work of Rankin and other authors, who established the same bound but with replaced by a constant. Again, see the previous post for a more detailed discussion. In ... [Link]

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