Blog Profile / Terence Tao's Blog

Filed Under:Academics / Mathematics
Posts on Regator:468
Posts / Week:1
Archived Since:December 12, 2008

Blog Post Archive

Maryam Mirzakhani

I am totally stunned to learn that Maryam Mirzakhani died today, aged 40, after a severe recurrence of the cancer she has been fighting for several years.  I had planned to email her some wishes for a speedy recovery after learning about the relapse yesterday; I still can’t fully believe that she didn’t make it. […]

On the universality of potential well dynamics

I’ve just uploaded to the arXiv my paper “On the universality of potential well dynamics“, submitted to Dynamics of PDE. This is a spinoff from my previous paper on blowup of nonlinear wave equations, inspired by some conversations with Sungjin Oh. Here we focus mainly on the zero-dimensional case of such equations, namely the potential […]

What are some useful, but little-known, features of the tools used in professional mathematics?

A few days ago, I was talking with Ed Dunne, who is currently the Executive Editor of Mathematical Reviews (and in particular with its online incarnation at MathSciNet).  At the time, I was mentioning how laborious it was for me to create a BibTeX file for dozens of references by using MathSciNet to locate each […]

Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges

Kaisa Matomaki, Maksym Radziwill, and I have uploaded to the arXiv our paper “Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges“, submitted to Proceedings of the London Mathematical Society. This paper is concerned with the estimation of correlations such as for medium-sized and large, where is the von Mangoldt […]

PCMI lecture notes on random matrix theory

In July I will be spending a week at Park City, being one of the mini-course lecturers in the Graduate Summer School component of the Park City Summer Session on random matrices.  I have chosen to give some lectures on least singular values of random matrices, the circular law, and the Lindeberg exchange method in […]

Quantitative continuity estimates

Suppose is a continuous (but nonlinear) map from one normed vector space to another. The continuity means, roughly speaking, that if are such that is small, then is also small (though the precise notion of “smallness” may depend on or, particularly if is not known to be uniformly continuous). If is known to […]

Generalisations of the limit functional

Suppose one has a bounded sequence of real numbers. What kinds of limits can one form from this sequence? Of course, we have the usual notion of limit, which in this post I will refer to as the classical limit to distinguish from the other limits discussed in this point. The classical limit, if […]

New bounds for Szemerédi’s theorem, III: A polylogarithmic bound for r_4(N)

Ben Green and I have (finally!) uploaded to the arXiv our paper “New bounds for Szemerédi’s theorem, III: A polylogarithmic bound for “, submitted to Mathematika. This is the sequel to two previous papers (and an erratum to the former paper), concerning quantitative versions of Szemerédi’s theorem in the case of length four progressions. This […]

Notes on nilcharacters and their symbols

A sequence of complex numbers is said to be quasiperiodic if it is of the form for some real numbers and continuous function. For instance, linear phases such as (where ) are examples of quasiperiodic sequences; the top order coefficient (modulo ) can be viewed as a “frequency” of the integers, and an element […]

Counting objects up to isomorphism: groupoid cardinality

How many groups of order four are there? Technically, there are an enormous number, so much so, in fact, that the class of groups of order four is not even a set, but merely a proper class. This is because any four objects can be turned into a group by designating one of the four […]

Yves Meyer wins the 2017 Abel Prize

Just a short post to note that Norwegian Academy of Science and Letters has just announced that the 2017 Abel prize has been awarded to Yves Meyer, “for his pivotal role in the development of the mathematical theory of wavelets”.  The actual prize ceremony will be at Oslo in May. I am actually in Oslo […]

Furstenberg limits of the Liouville function

Given a function on the natural numbers taking values in, one can invoke the Furstenberg correspondence principle to locate a measure preserving system – a probability space together with a measure-preserving shift (or equivalently, a measure-preserving -action on ) – together with a measurable function (or “observable”) that has essentially the same statistics as […]

Special cases of Shannon entropy

Given a random variable that takes on only finitely many values, we can define its Shannon entropy by the formula with the convention that. (In some texts, one uses the logarithm to base rather than the natural logarithm, but the choice of base will not be relevant for this discussion.) This is clearly a […]

A bound on partitioning clusters

Daniel Kane and I have just uploaded to the arXiv our paper “A bound on partitioning clusters“, submitted to the Electronic Journal of Combinatorics. In this short and elementary paper, we consider a question that arose from biomathematical applications: given a finite family of sets (or “clusters”), how many ways can there be of partitioning […]

Open thread for mathematicians on the immigration executive order

The self-chosen remit of my blog is “Updates on my research and expository papers, discussion of open problems, and other maths-related topics”.  Of the 774 posts on this blog, I estimate that about 99% of the posts indeed relate to mathematics, mathematicians, or the administration of this mathematical blog, and only about 1% are not […]

Some remarks on the lonely runner conjecture

I’ve just uploaded to the arXiv my paper “Some remarks on the lonely runner conjecture“, submitted to Contributions to discrete mathematics. I had blogged about the lonely runner conjecture in this previous blog post, and I returned to the problem recently to see if I could obtain anything further. The results obtained were more modest […]

AMS open math notes

I just learned (from Emmanuel Kowalski’s blog) that the AMS has just started a repository of open-access mathematics lecture notes.  There are only a few such sets of notes there at present, but hopefully it will grow in the future; I just submitted some old lecture notes of mine from an undergraduate linear algebra course […]

Finite time blowup for a supercritical defocusing nonlinear Schrodinger system

I’ve just uploaded to the arXiv my paper Finite time blowup for a supercritical defocusing nonlinear Schrödinger system, submitted to Analysis and PDE. This paper is an analogue of a recent paper of mine in which I constructed a supercritical defocusing nonlinear wave (NLW) system which exhibited smooth solutions that developed singularities in finite time. […]

Call for nominations for the 2018 Chern Medal

[This guest post is authored by Caroline Series.] The Chern Medal is a relatively new prize, awarded once every four years jointly by the IMU and the Chern Medal Foundation (CMF) to an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics. Funded by the CMF, the […]

An integration approach to the Toeplitz square peg problem

I’ve just uploaded to the arXiv my paper “An integration approach to the Toeplitz square peg problem“, submitted to Forum of Mathematics, Sigma. This paper resulted from my attempts recently to solve the Toeplitz square peg problem (also known as the inscribed square problem): Conjecture 1 (Toeplitz square peg problem) Let be a simple closed […]

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