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

Math News (1 - 25 of about 3030) (xml) (Feedlist)

## ICM2014 — Jim Arthur plenary lecturegowers

(27.08.2014 20:01h)

The main other thing I did on day two of the congress was go to a reception in the evening hosted by the French Embassy. It was less formal than that makes it sound, and as I circulated I met a number of people I hadn’t seen for quite a while, as well as others I had got to know at the congress itself. The French ambassador, who was disconcertingly young looking, gave a speech, as did Artur Avila as you know, Avila, like Ngo four years ago, is French , and one other person, whose name I’ve annoyingly forgotten. ... [Link]

## ICM2014 — Barak, Guralnick, Browngowers

(26.08.2014 19:29h)

Here’s a little puzzle to get this post started. Of the fourteen 21st-century Fields medallists if you count Perelman , seven — Lafforgue, Voevodsky, Tao, Werner, Smirnov, Avila and Mirzakhani — have something interesting in common that the others lack. What is this property? That’s a fairly easy question, so let’s follow it up with another one: how surprised should we be about this? Is there unconscious bias towards mathematicians with this property? Of this year’s 21 plenary lecturers, the only one with the property was Mirzakhani, and out of the 20 plenary lecturers in 2010, the only one with ... [Link]

## “Could a Quantum Computer Have Subjective Experience?”Scott

(25.08.2014 20:09h)

Author’s Note: Below is the prepared version of a talk that I gave two weeks ago at the workshop Quantum Foundations of a Classical Universe, which was held at IBM’s TJ Watson Research Center in Yorktown Heights, NY. My talk is for entertainment purposes only; it should not be taken seriously by anyone. If you reply in a way that makes clear you did take it seriously “I’m shocked and outraged that someone who dares to call himself a scientist would … [blah blah]“ , I will log your IP address, hunt you down at night, and force you to ... [Link]

## ICM2014 — Emmanuel Candès plenary lecturegowers

(25.08.2014 14:38h)

If you are a mathematical researcher, do you ever stop to ask yourself what the point is of all your research? Do you worry that the world could get along just fine without it? One person who doesn’t lose any sleep over doubts like this is Emmanuel Candès, who gave the second plenary lecture I went to. He began by talking a little about the motivation for the kinds of problems he was going to discuss, which one could summarize as follows: his research is worthwhile because it helps save the lives of children. More precisely, it used to be ... [Link]

## Why It MattersThe n-Category Café

(25.08.2014 04:23h)

One interesting feature of the Category Theory conference in Cambridge last month was that lots of the other participants started conversations with me about the whole-population, suspicionless surveillance that several governments are now operating. All but one were enthusiastically supportive of the work I’ve been doing to try to get the mathematical community to take responsibility for its part in this, and I appreciated that very much. The remaining one was a friend who wasn’t unsupportive, but said to me something like “I think I probably agree with you, but I’m not sure. I don’t see why it matters. Persuade ... [Link]

## My office in 1870Kowalski

(23.08.2014 18:23h)

The historical “main” building of ETH was finished 150 years ago, in 1864. Or rather, the first version was finished, since it was altered and extended quite a bit since then as did the surroundings! . In a recent NZZ article, I saw this picture ETH in 1870 of the building as it looked in 1870. The red square indicates where my office is located… [Link]

## ICM2014 — Ian Agol plenary lecturegowers

(22.08.2014 19:19h)

On the second day of the congress I hauled myself out of bed in time, I hoped, to have a shower and find some breakfast before the first plenary lecture of the congress started at 9am. The previous day in the evening I had chanced upon a large underground shopping mall directly underneath the conference centre, so I thought I’d see if I could find some kind of café there. However, at 8:30 in the morning it was more or less deserted, and I found myself wandering down very long empty passages, constantly looking at my watch and worrying that ... [Link]

## Large gaps between consecutive prime numbersTerence Tao

(22.08.2014 05:46h)

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

(21.08.2014 06:23h)

[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]

## Holy Crap, Do You Know What A Compact Ring Is?The n-Category Café

(21.08.2014 00:54h)

You know how sometimes someone tells you a theorem, and it’s obviously false, and you reach for one of the many easy counterexamples only to realize that it’s not a counterexample after all, then you reach for another one and another one and find that they fail too, and you begin to concede the possibility that the theorem might not actually be false after all, and you feel your world start to shift on its axis, and you think to yourself: “Why did no one tell me this before?” That’s what happened to me today, when my PhD student Barry ... [Link]

## ICM2014 — Khot laudatiogowers

(20.08.2014 16:00h)

After McMullen’s laudatio on Mirzakhani, it was time for Sanjeev Arora to talk about the work of the Nevanlinna prize winner Subhash Khot. It was also the time that a significant proportion of the audience decided that enough was enough and left the room. The same thing happened in Hyderabad four years ago, and on both occasions I was fairly shocked: I think it shows a striking disrespect, not so much for the speaker and prizewinner, though there is that aspect too, as for theoretical computer science in general. It seems to say, “Right, that’s the interesting prizes over — ... [Link]

## ICM2014 — Mirzakhani laudatiogowers

(19.08.2014 14:42h)

I’m going to try the same exercise with Curt McMullen’s talk about Mirzakhani’s work that I did with Ofer Zeitouni’s about Hairer: that is, I’ll begin by seeing what I can remember if I don’t look at my notes. However, I remember disoncertingly little, and what I do remember is somewhat impressionistic. The most concrete thing I remember without being 100% sure I’ve got it right is that one of Mirzakhani’s major results concerns counting closed geodesics in Riemann surfaces. A geodesic is roughly speaking a curve that feels like a straight line to an inhabitant of the surface. Another ... [Link]

## ICM2014 — Hairer laudatiogowers

(18.08.2014 19:58h)

I haven’t kept up anything like the frequency of posts at this ICM that I managed at the last one. There are at least three reasons for this. One is that I was in the middle of writing up a result, so I devoted some of my rare free moments to that. Another is that the schedule was so full of good talks that I hardly skipped any sessions. And the third is that on the last day I was taken ill: I won’t go into too much detail, but let’s say that what I had sort of rhymed with ... [Link]

## Art in the life of mathematiciansIzabella Laba

(18.08.2014 02:04h)

This book has been in the works for some years now, and I’m thrilled to finally have a demo copy to show you. The book will be published by the American Mathematical Society. The demo copy has been produced impressively quickly! by the Hungarian publisher Ab Ovo. I’m very grateful to Anna Kepes Szemerédi for envisioning this project in the first place, and for all the hard work she has put into it. I have contributed an essay on photography. You can download it here, and here is the gallery of the photos I offered to be used in the ... [Link]

## Subhash Khot’s prizewinning researchScott

(17.08.2014 01:21h)

I already congratulated Subhash Khot in my last post for winning the Nevanlinna Award, but this really deserves a separate post. Khot won theoretical computer science’s highest award largely for introducing and exploring the Unique Games Conjecture UGC , which says in one sentence that a large number of the approximation problems that no one has been able to prove NP-hard, really are NP-hard. In particular, if the UGC is true, then for MAX-CUT and dozens of other important optimization problems, no polynomial-time algorithm can always get you closer to the optimal solution than some semidefinite-programming-based algorithm gets you, unless ... [Link]

## talk slidesICM update

(15.08.2014 23:33h)

Since a number of people asked, here are the slides from my ICM talk yesterday. I have also posted them on my preprints page. I believe the talk was recorded and the video will presumably be available from the ICM webpage. Alternatively, you can read my ICM proceedings paper for a longer version. [Link]

## ICM2014 — Bhargava laudatiogowers

(15.08.2014 20:46h)

I ended up writing more than I expected to about Avila. I’ll try not to fall into the same trap with Bhargava, not because there isn’t lots to write about him, but simply because if I keep writing at this length then by the time I get on to some of the talks I’ve been to subsequently I’ll have forgotten about them. Dick Gross also gave an excellent talk. He began with some of the basic theory of binary quadratic forms over the integers, that is, expressions of the form . One assumes that they are primitive meaning that , ... [Link]

## Mathematical GymnasticsGil Kalai

(15.08.2014 13:52h)

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]

## Upcoming booksKowalski

(15.08.2014 08:38h)

As the summer vacations draw to a close, I’d like to point to two upcoming AMS books which might, hopefully, interest some readers… 1 My lecture notes on representation theory expanded will appear in September, published in the Graduate Studies in Mathematics series; the preview material contains Chapter 1, and a fair bit of Chapter 2; the index is also available, and perusing it will give an idea of the range of topics mentioned. 2 Henryk Iwaniec has also a new book coming, in October, containing his lectures notes on the Riemann zeta function. I haven’t seen it yet, but ... [Link]

## ICM2014 — Avila laudatiogowers

(14.08.2014 20:57h)

As I said in my previous post, I don’t think I’m going to try all that hard to explain the work of the prizewinners, since it has been very well explained in other places except that much more attention has gone to the Fields medallists than to the Nevanlinna prize winner — maybe I’ll try to redress the balance a little bit there . Instead, I’d just like to mention a few things that I found interesting or amusing during the laudationes. The first one was an excellent talk by Etienne Ghys on the work of Artur Avila. The only ... [Link]

## Khot, Osher, GriffithsTerence Tao

(14.08.2014 09:29h)

In addition to the Fields medallists mentioned in the previous post, the IMU also awarded the Nevanlinna prize to Subhash Khot, the Gauss prize to Stan Osher my colleague here at UCLA! , and the Chern medal to Phillip Griffiths. Like I did in 2010, I’ll try to briefly discuss one result of each of the prize winners, though the fields of mathematics here are even further from my expertise than those discussed in the previous post and all the caveats from that post apply here also . Subhash Khot is best known for his Unique Games Conjecture, a problem ... [Link]

## ICM2014 — opening ceremonygowers

(13.08.2014 19:21h)

I’d forgotten just how full the first day of an ICM is. First, you need to turn up early for the opening ceremony, so you end up sitting around for an hour and half or so before it even starts. Then there’s the ceremony itself, which lasts a couple of hours. Then in the afternoon you have talks about the four Fields Medallists and the Nevanlinna Prize winner, with virtually no breaks. Then after a massive ten minutes, the Nevanlinna Prize winner talks about his in this case own work, about which you have just heard, but in a bit ... [Link]

## “For the first time ever…”Media Item from “Haaretz” Today

(13.08.2014 18:12h)

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]

## no. Is the P vs. NP problem ill-posed? Answer

(13.08.2014 16:15h)

A couple days ago, a reader wrote to me to ask whether it’s possible that the solution to the P vs. NP problem is simply undefined—and that one should enlarge the space of possible answers using non-classical logics the reader mentioned something called Catuṣkoṭi logic . Since other people have emailed me with similar questions in the past, I thought my response might be of more general interest, and decided to post it here. Thanks for your mail! I’m afraid I don’t agree with you that there’s a problem in the formulation of P vs. NP. Let me come at ... [Link]

## Avila, Bhargava, Hairer, MirzakhaniTerence Tao

(13.08.2014 14:04h)

The 2014 Fields medallists have just been announced as in alphabetical order of surname Artur Avila, Manjul Bhargava, Martin Hairer, and Maryam Mirzakhani see also these nice video profiles for the winners, which is a new initiative of the IMU and the Simons foundation . This time four years ago, I wrote a blog post discussing one result from each of the 2010 medallists; I thought I would try to repeat the exercise here, although the work of the medallists this time around is a little bit further away from my own direct area of expertise than last time, and ... [Link]

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