### Description

This site is currently hosting\n\nupdates on my mathematical research;\nexpository articles (such as my articles for the Princeton Companion to Mathematics, or for the tricks wiki);\ndiscussion of open problems;\ntalks that I have given or attended (such as the Distinguished Lectures Series at UCLA);\nmy advice on mathematical careers and mathematical writing;\ninformation about my books;\nmy lecture notes on ergodic theory, on the Poincar conjecture, on random matrices, on graduate real analysis (245B and 245C), and on higher order Fourier analysis;\na campaign to support mathematics, statistics, and computing at the University of Southern Queensland;\nand various other topics, usually related to mathematics.\nWhile most of the posts are aimed at those with a graduate maths background, I will also occasionally have a number of non-technical posts aimed at a lay mathematical audience. My selection of topics is guided by my own personal taste; I do not take requests for specific topics to post about on this blog.

### What's new (with Terry Tao)'s Latest Posts

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In analytic number theory, an arithmetic function is simply a function from the natural numbers to the real or complex numbers. (One occasionally also considers arithmetic functions taking values in more general rings than or , as in this previous blog post, but we will restrict attention here to the classical situation of real or […]

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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 […]

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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 […]

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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 […]

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