### 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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We continue the discussion of sieve theory from Notes 4, but now specialise to the case of the linear sieve in which the sieve dimension is equal to , which is one of the best understood sieving situations, and one of the rare cases in which the precise limits of the sieve method are known. […]

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Many problems in non-multiplicative prime number theory can be recast as sieving problems. Consider for instance the problem of counting the number of pairs of twin primes contained in for some large ; note that the claim that for arbitrarily large is equivalent to the twin prime conjecture. One can obtain this count by any […]

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A fundamental and recurring problem in analytic number theory is to demonstrate the presence of cancellation in an oscillating sum, a typical example of which might be a correlation between two arithmetic functions and , which to avoid technicalities we will assume to be finitely supported (or that the variable is localised to a finite […]

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We now move away from the world of multiplicative prime number theory covered in Notes 1 and Notes 2, and enter the wider, and complementary, world of non-multiplicative prime number theory, in which one studies statistics related to non-multiplicative patterns, such as twins . This creates a major jump in difficulty; for instance, even the […]

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