Math News July 20th, 2009
Patrick Stein

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

Math News (26 - 50 of about 3165) (xml) (Feedlist)


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]

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]

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]

Long gaps between primesTerence Tao
(17.12.2014 10:25h)

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]

Hyperbolic SurfacesCharles Siegel
(17.12.2014 08:55h)

Ok, with the hyperbolic plane and its metric and geodesics out of the way, we can start getting into some surface theory. Definition: A hyperbolic surface of genus g is a topological surface of genus g along with a metric that is locally isometric to the hyperbolic plane. Equivalently, it has a Riemannian metric of constant curvature -1. There are some distinguished types of curves on a hyperbolic surface, and I don’t just mean the geodesics though we’ll relate them to geodesics . This is going to be a definition heavy post, but hey, we’re doing a construction, this tends ... [Link]

The Turing movieScott
(17.12.2014 04:36h)

Last week I finally saw The Imitation Game, the movie with Benedict Cumberbatch as Alan Turing. OK, so for those who haven’t yet seen it: should you? Here’s my one paragraph summary: imagine that you told the story of Alan Turing—one of the greatest triumphs and tragedies of human history, needing no embellishment whatsoever—to someone who only sort-of understood it, and who filled in the gaps with weird fabrications and Hollywood clichés. And imagine that person retold the story to a second person, who understood even less, and that that person retold it to a third, who understood least of ... [Link]

Walter LewinScott
(10.12.2014 17:25h)

Yesterday I heard the sad news that Prof. Walter Lewin, age 78—perhaps the most celebrated physics teacher in MIT’s history—has been stripped of his emeritus status and barred from campus, and all of his physics lectures removed from OpenCourseWare, because an internal investigation found that he had been sexually harassing students online. I don’t know anything about what happened beyond the terse public announcements, but those who do know tell me that the charges were extremely serious, and that “this wasn’t a borderline case.” I’m someone who feels that sexual harassment must never be tolerated, neither here nor anywhere else. ... [Link]

Random matrices have simple spectrumTerence Tao
(08.12.2014 06:01h)

Van Vu and I have just uploaded to the arXiv our paper “Random matrices have simple eigenvalues“. Recall that an Hermitian matrix is said to have simple eigenvalues if all of its eigenvalues are distinct. This is a very typical property of matrices to have: for instance, as discussed in this previous post, in the space of all Hermitian matrices, the space of matrices without all eigenvalues simple has codimension three, and for real symmetric cases this space has codimension two. In particular, given any random matrix ensemble of Hermitian or real symmetric matrices with an absolutely continuous distribution, we ... [Link]

Random matrices have simple spectrumTerence Tao
(05.12.2014 03:34h)

Van Vu and I have just uploaded to the arXiv our paper “Random matrices have simple eigenvalues“. Recall that an Hermitian matrix is said to have simple eigenvalues if all of its eigenvalues are distinct. This is a very typical property of matrices to have: for instance, as discussed in this previous post, in the space of all Hermitian matrices, the space of matrices without all eigenvalues simple has codimension three, and for real symmetric cases this space has codimension two. In particular, given any random matrix ensemble of Hermitian or real symmetric matrices with an absolutely continuous distribution, we ... [Link]

The hyperbolic planeCharles Siegel
(03.12.2014 20:49h)

So, I know I usually talk about strictly algebraic geometry stuff, but the moduli of curves lives in an interesting place. It’s both an algebraic and an analytic object. So we’re going to start by talking a bit about hyperbolic surfaces, as we work towards a construction of Teichmüller space, which is used to construct the moduli of curves over . We actually have to start with some more basic differential geometric notions that have been neglected, because we never did a “Differential Geometry from the Beginning” series perhaps I should in the future? Chime in in the comments if ... [Link]

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]

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