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

Math News (1 - 25 of about 2977) (xml) (Feedlist)

## Pullbacks That Preserve Weak EquivalencesThe n-Category Café

(21.07.2014 23:33h)

The following concept seems to have been reinvented a bunch of times by a bunch of people, and every time they give it a different name. Definition: Let CC be a category with pullbacks and a class of weak equivalences. A morphism f:A→Bf:A\to B is a [insert name here] if the pullback functor f *:C/B→C/Af^\ast:C/B \to C/A preserves weak equivalences. In a right proper model category, every fibration is one of these. But even in that case, there are usually more of these than just the fibrations. There is of course also a dual notion in which pullbacks are replaced ... [Link]

## Variants of the Selberg sieve, and bounded intervals containing many primesTerence Tao

(21.07.2014 15:11h)

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 Place of Diversity in Pure MathematicsThe n-Category Café

(20.07.2014 14:40h)

Nope, this isn’t about gender or social balance in math departments, important as those are. On Friday, Glasgow’s interdisciplinary Boyd Orr Centre for Population and Ecosystem Health — named after the whirlwind of Nobel-Peace-Prize-winning scientific energy that was John Boyd Orr — held a day of conference on diversity in multiple biological senses, from the large scale of rainforest ecosystems right down to the microscopic scale of pathogens in your blood. I used my talk slides here to argue that the concept of diversity is fundamentally a mathematical one, and that, moreover, it is closely related to core mathematical quantities ... [Link]

## Mini-monomathgowers

(19.07.2014 22:45h)

The title of this post is a nod to Terry Tao’s four mini-polymath discussions, in which IMO questions were solved collaboratively online. As the beginning of what I hope will be a long exercise in gathering data about how humans solve these kinds of problems, I decided to have a go at one of this year’s IMO problems, with the idea of writing down my thoughts as I went along. Because I was doing that and doing it directly into a LaTeX file rather than using paper and pen , I took quite a long time to solve the problem: ... [Link]

## The Ten-Fold WayThe n-Category Café

(19.07.2014 12:03h)

There are 10 of each of these things: Associative real super-division algebras. Classical families of compact symmetric spaces. Ways that Hamiltonians can get along with time reversal TT and charge conjugation CC symmetry. Dimensions of spacetime in string theory. It’s too bad nobody took up writing This Week’s Finds in Mathematical Physics when I quit. Someone should have explained this stuff in a nice simple way, so I could read their summary instead of fighting my way through the original papers. I don’t have much time for this sort of stuff anymore! Luckily there are some good places to read ... [Link]

## Special Day on Quantum PCP, Quantum Codes, Simplicial Complexes and Locally Testable CodesNext Week in Jerusalem

(16.07.2014 15:56h)

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]

## A RoundupMath and Mass Surveillance

(16.07.2014 00:01h)

The Notices of the AMS has just published the second in its series “Mathematicians discuss the Snowden revelations”. The first was here. The introduction to the second article cites this blog for “a discussion of these issues”, but I realized that the relevant posts might be hard for visitors to find, scattered as they are over the last eight months. So here, especially for Notices readers, is a roundup of all the posts and discussions we’ve had on the subject. In reverse chronological order: Should mathematicians cooperate with GCHQ? Part 3 Should mathematicians cooperate with GCHQ? Part 2 New Scientist ... [Link]

## Seth Teller 1964-2014 Scott

(11.07.2014 18:42h)

Seth Teller was a colleague of mine in CSAIL and the EECS department, and was one of my favorite people in all of MIT. He was a brilliant roboticist, who among many other things spearheaded MIT’s participation in the DARPA Grand Challenge for self-driving cars, and who just recently returned from a fact-finding trip to Fukushima, Japan, to see how robots could help in investigating the damaged reactor cores there. I saw Seth twice a week at lab and department lunches, and he often struck up conversations with me about quantum computing, cosmology, and other things. His curiosity was immense, ... [Link]

## The parity problem obstruction for the binary Goldbach problem with bounded errorTerence Tao

(10.07.2014 15:19h)

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]

## Describing PROPs Using Generators and RelationsThe n-Category Café

(10.07.2014 12:04h)

Here’s another post asking for a reference to stuff that should be standard. The last ones succeeded wonderfully, so thanks! I should be able to say CC is the symmetric monoidal category with the following presentation: it’s generated by objects xx and yy and morphisms L:x⊗y→yL: x \otimes y \to y and R:y⊗x→yR: y \otimes x \to y, with the relation L⊗1 1⊗R α x,y,x= 1⊗R L⊗1 L \otimes 1 1 \otimes R \alpha_{x,y,x} = 1 \otimes R L \otimes 1 Here α\alpha is the associator. Don’t worry about the specific example: I’m just talking about a presentation of a ... [Link]

## Happy Birthday Ervin, JÃ¡nos, PÃ©ter, and Zoli!Gil Kalai

(09.07.2014 19:56h)

The four princes in summit 200, ten years ago. Left to right Ervin Győri, Zoltán Füredi, Péter Frankl and János Pach In 2014, Péter Frankl, Zoltán Füredi, Ervin Győri and János Pach are turning 60 and summit 240 is a conference this week in Budapest to celebrate the birthday of those ever-young combinatorics princes. I know the four guys for about 120 years. I first met Peter and Janos together I think in Paris in 1979, then Zoli at MIT in 1985 and I met Ervin in the mid late 90s in Budapest. Noga Alon have recently made the observation ... [Link]

## Hilbert’s fifth problem and approximate groupsTerence Tao

(09.07.2014 03:52h)

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]

## The Categorical Origins of Lebesgue IntegrationThe n-Category Café

(08.07.2014 01:24h)

I’ve just come back from the big annual-ish category theory meeting, Category Theory 2014 in Cambridge, also attended by Café hosts Emily and Simon. The talk I gave there was called The categorical origins of Lebesgue integration — click for slides — and I’ll briefly describe it now. There are two theorems. Theorem A The Banach space L 1[0,1]L^1[0, 1] has a simple universal property. This leads to a unique characterization of integration on [0,1][0, 1]. Theorem B The functor L 1:L^1: finite measure spaces →\to Banach spaces has a simple universal property. This leads to a unique characterization of ... [Link]

## The subspace theorem approach to Siegel’s theorem on integral points on curves via nonstandard analysisTerence Tao

(07.07.2014 20:20h)

[Link]

## My Mathematical Dialogue with Jürgen EckhoffGil Kalai

(07.07.2014 15:44h)

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]

## How Many Women?Test Your Intuition 23

(07.07.2014 15:44h)

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='https://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]

## Happy Birthday Richard Stanley!Gil Kalai

(07.07.2014 15:44h)

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]

## Happy Birthday Ervin, János, Péter, and Zoli!Gil Kalai

(06.07.2014 13:16h)

The four princes in summit 200, ten years ago. Left to right Ervin Győri, Zoltán Füredi, Péter Frankl and János Pach In 2014, Péter Frankl, Zoltán Füredi, Ervin Győri and János Pach are turning 60 and summit 240 is a conference this week in Budapest to celebrate the birthday of those ever-young combinatorics princes. I know the four guys for about 120 years. I first met Peter and Janos together I think in Paris in 1979, then Zoli at MIT in 1985 and I met Ervin in the mid late 90s in Budapest. Noga Alon have recently made the observation ... [Link]

## Meta-statisticsKowalski

(05.07.2014 20:53h)

One of the most unfortunate developments of modern football, and a clear symptom of the decline of civilization, is the regrettable irruption in the comments of a deluge of factoids that manage to simultaneously give a bad name to team sports and to statistics “This is the first time in twenty-one competitive games played in the Southern Hemisphere that a French Number 10 player’s backward pass from the left foot has been intercepted by a Dutch player born in Amsterdam” . Roger Couderc certainly did not need this to make a game come to life of course, technically, he was ... [Link]

## What makes the Monster Lie Algebra special?Scott Carnahan

(05.07.2014 19:37h)

This is a post I’d been meaning to write for several years, but I was finally prompted to action after talking to some confused physicists. The Monster Lie Algebra, as a Lie algebra, has very little structure – it or rather, its positive subalgebra is quite close to being free on countably infinitely many generators. In addition to its Lie algebra structure, it has a faithful action of the monster simple group by Lie algebra automorphisms. However, the bare fact that the monster acts faithfully on the Lie algebra by diagram automorphisms is not very interesting: the almost-freeness means that ... [Link]

## Elsevier in AustraliaScott Morrison

(05.07.2014 19:37h)

I’ve just got back from talking to Roxanne Missingham, the University Librarian here at ANU, about Elsevier, and I want to quickly report on what I learnt. I don’t yet have any of the juicy numbers revealing what libraries are paying for their Elsevier subscriptions as Timothy Gowers has been doing in the UK; if you haven’t read his post do that first! . Nevertheless there are some interesting details. Essentially all the Australian universities, excepting a few tiny private institutes, subscribe to the Freedom collection this is the same bundle that nearly everyone is forced into subscribing to . ... [Link]

## The many principles of conservation of numberDavid Speyer

(05.07.2014 19:37h)

In algebraic geometry, we like to make statements like: “two conics meet at points”, “a degree four plane curve has bitangents”, “given four lines in three space, there are lines that meet all of them”. In each of these, we are saying that, as some parameter the conics, the degree four curve, the lines changes, the number of solutions to some equation stays constant. The “principle of conservation of number” refers to various theorems which make this precise. In my experience, students in algebraic geometry tend to pick up the rough idea but remain hazy on the details, most likely ... [Link]

## 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]

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