Math News July 20th, 2009
Patrick Stein

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

Math News (26 - 50 of about 3143) (xml) (Feedlist)


A general parity problem obstructionTerence Tao
(01.12.2014 13:43h)

Many problems and results in analytic prime number theory can be formulated in the following general form: given a collection of affine- linear forms , none of which is a multiple of any other, find a number such that a certain property of the linear forms are true. For instance: For the twin prime conjecture, one can use the linear forms , , and the property in question is the assertion that and are both prime. For the even Goldbach conjecture, the claim is similar but one uses the linear forms , for some even integer . For Chen’s theorem, ... [Link]

Analytic prime number theory254A announcement
(01.12.2014 13:43h)

In the winter quarter starting January 5 I will be teaching a graduate topics course entitled “An introduction to analytic prime number theory“. As the name suggests, this is a course covering many of the analytic number theory techniques used to study the distribution of the prime numbers . I will list the topics I intend to cover in this course below the fold. As with my previous courses, I will place lecture notes online on my blog in advance of the physical lectures. The type of results about primes that one aspires to prove here is well captured by ... [Link]

Discretised wave equationsTerence Tao
(01.12.2014 13:43h)

The wave equation is usually expressed in the form where is a function of both time and space , with being the Laplacian operator. One can generalise this equation in a number of ways, for instance by replacing the spatial domain with some other manifold and replacing the Laplacian with the Laplace-Beltrami operator or adding lower order terms such as a potential, or a coupling with a magnetic field . But for sake of discussion let us work with the classical wave equation on . We will work formally in this post, being unconcerned with issues of convergence, justifying interchange ... [Link]

A Confession of Mathematical ErrorsPostBQP Postscripts
(01.12.2014 00:41h)

tl;dr: This post reveals two errors in one of my most-cited papers, and also explains how to fix them. Thanks to Piotr Achinger, Michael Cohen, Greg Kuperberg, Ciaran Lee, Ryan O’Donnell, Julian Rosen, Will Sawin, Cem Say, and others for their contributions to this post. If you look at my Wikipedia page, apparently one of the two things in the world that I’m “known for” along with algebrization is “quantum Turing with postselection.” By this, Wikipedia means my 2004 definition of the complexity class PostBQP—that is, the class of decision problems solvable in bounded-error quantum polynomial time, assuming the ability ... [Link]

Lens of Computation on the SciencesScott
(25.11.2014 23:32h)

This weekend, the Institute for Advanced Study in Princeton hosted a workshop on the “Lens of Computation in the Sciences,” which was organized by Avi Wigderson, and was meant to showcase theoretical computer science’s imperialistic ambitions to transform every other field. I was proud to speak at the workshop, representing CS theory’s designs on physics. But videos of all four of the talks are now available, and all are worth checking out: Computational Phenomena in Biology, by Leslie Valiant Computational Phenomena in Economics, by Tim Roughgarden Computational Phenomena in Social Science, by Jon Kleinberg Computational Phenomena in Physics, by me ... [Link]

Proust, my family and AustraliaKowalski
(25.11.2014 17:10h)

When I was reading Proust, I noted with some amusement the character named simply “Ski” in the first volume of his appearance, a sculptor and amateur musician who is later revealed to be properly called “Viradobetski”, an actual name which was too complicated for the dear Madame Verdurin to try to remember. I just learnt from my better educated brother that Proust s’est inspiré d’Henri Kowalski né en 1841, fils d’un officier polonais émigré en Bretagne. Il était à la fois compositeur de musique et concertiste. or Proust used as model Henri Kowalski, born in 1841, son of a Polish ... [Link]

Kuperberg’s parableScott
(24.11.2014 00:04h)

Recently, longtime friend-of-the-blog Greg Kuperberg wrote a Facebook post that, with Greg’s kind permission, I’m sharing here. A parable about pseudo-skepticism in response to climate science, and science in general. Doctor: You ought to stop smoking, among other reasons because smoking causes lung cancer. Patient: Are you sure? I like to smoke. It also creates jobs. D: Yes, the science is settled. P: All right, if the science is settled, can you tell me when I will get lung cancer if I continue to smoke? D: No, of course not, it’s not that precise. P: Okay, how many cigarettes can ... [Link]

A general parity problem obstructionTerence Tao
(22.11.2014 11:27h)

Many problems and results in analytic prime number theory can be formulated in the following general form: given a collection of affine- linear forms , none of which is a multiple of any other, find a number such that a certain property of the linear forms are true. For instance: For the twin prime conjecture, one can use the linear forms , , and the property in question is the assertion that and are both prime. For the even Goldbach conjecture, the claim is similar but one uses the linear forms , for some even integer . For Chen’s theorem, ... [Link]

Moduli of Riemann SurfacesNew Series
(21.11.2014 03:14h)

Though I’m not quite ready to start next week! I feel that, in the spirit of Jim getting back to the blogging and my continued promises, I’d announce my series now. I’m going to start a detailed series on the moduli of Riemann surfaces, including both topological and geometric aspects. And I figured I’d start it out with a list of references for some of the topics that I’d be covering: Books Algebraic Curves and Riemann Surfaces by Miranda Geometry of Algebraic Curves Volumes I and II by Arbarello, Cornalba, Griffiths and Harris Geometric Invariant Theory by Mumford, Fogarty and ... [Link]

On proof and progress in feminismIzabella Laba
(20.11.2014 04:45h)

The recent allegations against several celebrities have led to a broader conversation on how we, as a society, don’t believe women. In a “he said, she said” situation, we trust the man and assume that the woman is either mistaken or lying. “Taking us seriously” means that we are advised of such and offered an explanation for our dismissal instead of simply being dismissed outright. It’s not only personal bias, conscious or not; there are institutional mechanisms perpetuating this state of affairs. No proof is ever sufficient if it comes from a woman. Should she present multiple affidavits, all signed ... [Link]

ANU hiring postdocsScott Morrison
(20.11.2014 01:06h)

Amnon Neeman has just put up an ad for two postdoctoral positions at the ANU. He says: “The successful applicants should have strong research interests and activities in or related to one of the following fields: Algebraic Geometry, Commutative Algebra, Representation Theory, Algebraic Topology, Algebraic K-Theory. Skills at applying the techniques of triangulated categories to these areas would be a plus.” These are excellent positions — available for up to 3 years, with no teaching requirements, and salaries in the AUD81-89k range. Applications close at the end of January, and I hear Amnon is keen to hire as soon as ... [Link]

ICERM postdoctoral positionsIzabella Laba
(16.11.2014 22:17h)

I’m co-organizing the program Dimension and Dynamics at the Institute for Computational and Experimental Research in Mathematics in Spring 2016. Yes, this means that I hope to participate in the program. Details to follow when they are finalized. ICERM has several postdoctoral positions associated with the program, one for the full academic year and four for the semester. Applications should be submitted via MathJobs. There is also funding for program visitors and workshop participants; the ICERM webpage has more details on that. The program covers various aspects of dimension theory and dynamics, from ergodic theory to hyperbolic dynamics to computation. ... [Link]

What does the NSA think of academic cryptographers? Recently-declassified document provides cluesScott
(16.11.2014 15:11h)

Brighten Godfrey was one of my officemates when we were grad students at Berkeley. He’s now a highly-successful computer networking professor at the University of Illinois Urbana-Champaign, where he studies the wonderful question of how we could get the latency of the Internet down to the physical limit imposed by the finiteness of the speed of light. Right now, we’re away from that limit by a factor of about 50. Last week, Brighten brought to my attention a remarkable document: a 1994 issue of CryptoLog, an NSA internal newsletter, which was recently declassified with a few redactions. The most interesting ... [Link]

Der QuantencomputerScott
(14.11.2014 15:16h)

Those of you who read German I don’t might enjoy a joint interview of me and Seth Lloyd about quantum computing, which was conducted in Seth’s office by the journalist Christian Meier, and published in the Swiss newspaper Neue Zürcher Zeitung. Even if you don’t read German, you can just feed the interview into Google Translate, like I did. While the interview covers ground that will be forehead-bangingly familiar to regular readers of this blog, I’m happy with how it turned out; even the slightly-garbled Google Translate output is much better than most quantum computing articles in the English-language press. ... [Link]

Analytic prime number theory254A announcement
(14.11.2014 12:02h)

In the winter quarter starting January 5 I will be teaching a graduate topics course entitled “An introduction to analytic prime number theory“. As the name suggests, this is a course covering many of the analytic number theory techniques used to study the distribution of the prime numbers . I will list the topics I intend to cover in this course below the fold. As with my previous courses, I will place lecture notes online on my blog in advance of the physical lectures. The type of results about primes that one aspires to prove here is well captured by ... [Link]

Grothendieck 1928-2014Scott Morrison
(13.11.2014 23:57h)

http://www.liberation.fr/sciences/2014/1~ [Link]

Which of the following three groups is trivialTest your intuition 24
(13.11.2014 05:54h)

Martin Bridson We have three finitely presented groups A is generated by two generators a and b and one relation B is generated by three generators a, b, c and three relations , . C is generated by four generators a, b, c, d and four relations , , and . Test your intuition: which of the groups A, B or C is trivial Please do not answer this poll if you already knew the answer Take Our Poll function d,c,j {if !d.getElementById j {var pd=d.createElement c ,s;pd.id=j;pd.src='http://s1.wp.com/~ c [0];s.parentNode.insertBefore pd,s ;} else if typeof jQuery !=='undefined' jQuery d.body .trigger ... [Link]

School Starts at HUJIGil Kalai
(12.11.2014 03:50h)

We are now starting the third week of the academic year at HUJI. As usual, things are very hectic, a lot of activities in the mathematics department, in our sister CS department, around in the campus, and in our combinatorics group. A lot is also happening in other universities around. This semester I am teaching a course on “Social Choice and some Topics from Cooperative Game Theory” in our Federmann Center for the Study of Rationality. I will probably create a page for the course in the near future. During the summer we ran an informal multi-university research activity on ... [Link]

Interstellar’s dangling wormholesScott
(10.11.2014 20:49h)

Update Nov. 15 : A third of my confusions addressed by reading Kip Thorne’s book! Details at the bottom of this post. On Saturday Dana and I saw Interstellar, the sci-fi blockbuster co-produced by the famous theoretical physicist Kip Thorne who told me about his work on this movie when I met him eight years ago . We had the rare privilege of seeing the movie on the same day that we got to hang out with a real astronaut, Dan Barry, who flew three shuttle missions and did four spacewalks in the 1990s. As the end result of a ... [Link]

The torsion on CM elliptic curves over prime degree number fieldsJim Stankewicz
(07.11.2014 14:31h)

It’s good to be back! This weekend I’m going to Paris to give a talk in the London-Paris Number Theory seminar so I’m going to give a preview of that talk, based on joint work with Pete Clark and Abbey Bourdon. We will post this onto the arxiv soon. Of course the paper is about the torsion in certain kinds of elliptic curves. The landmark result in this direction is of course Mazur’s theorem, stating that if is any elliptic curve over then the torsion subgroup of is isomorphic to an element of the following: Moreover each group occurs as ... [Link]

Discretised wave equationsTerence Tao
(06.11.2014 12:40h)

The wave equation is usually expressed in the form where is a function of both time and space , with being the Laplacian operator. One can generalise this equation in a number of ways, for instance by replacing the spatial domain with some other manifold and replacing the Laplacian with the Laplace-Beltrami operator or adding lower order terms such as a potential, or a coupling with a magnetic field . But for sake of discussion let us work with the classical wave equation on . We will work formally in this post, being unconcerned with issues of convergence, justifying interchange ... [Link]

Sums of kth powersgowers
(05.11.2014 04:18h)

Recently I was giving a talk at a school in London and had cause to think about sums of kth powers, because I wanted to show people the difference between unenlightening proofs and enlightening ones. My brief was to try to give them some idea of what proofs are and why they are worth bothering about. On the train down, I realized that there is a very simple general argument that can be used to work out formulae for sums of kth powers. After a brief look online, I haven’t found precisely this method, though I’ve found plenty of methods ... [Link]

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