Math News July 20th, 2009
Patrick Stein

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

Math News (26 - 50 of about 3045) (xml) (Feedlist)

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]

ICM2014 — first impressionsgowers
(13.08.2014 03:15h)

I’m writing this at 6:22am in my hotel room in Seoul, which is in a hotel that is right next to the conference centre, to the point where you don’t have to go out of doors to get from one to the other. I’ve just had a good night’s sleep, even though in French time which is what I was used to until the day before yesterday — if that concept still means anything my entire night has been during the day time, and now is about the time I’d be thinking of going to bed. I feel a bit ... [Link]

Maryam Mirzakhani makes historyIzabella Laba
(12.08.2014 20:54h)

The IMU has just announced this year’s Fields medal winners. For the first time ever, a Fields medal has been awarded to a woman, Maryam Mirzakhani. I will have the honour of attending the ceremony this morning. The official press release on Mirzakhani’s research is available, as are the citations for the other Fields medalists. I’d like to speak to what the selection of a female Fields medalist means to me as a woman and a mathematician. In that, I would like to paraphrase something that Melissa Harris-Perry has said about the election of President Obama. Mirzakhani’s selection does exactly ... [Link]

The Ten-Fold Way Part 4 The n-Category Café
(12.08.2014 02:46h)

Back in 2005, Todd Trimble came out with a short paper on the super Brauer group and super division algebras, which I’d like to TeXify and reprint here. In it, he gives extremely efficient proofs of several facts I alluded to last time. Namely: • There are exactly 10 real division superalgebras. • 8 of them have center ℝ\mathbb{R}, and these are Morita equivalent to the real Clifford algebras Cliff 0,…,Cliff 7Cliff_0, \dots, Cliff_7. • 2 of them have center ℂ\mathbb{C}, and these are Morita equivalent to the complex Clifford algebras ℂliff 0\mathbb{C}liff_0 and ℂliff 1\mathbb{C}liff_1. • The real Clifford ... [Link]

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]

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