What's new (with Terry Tao)
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
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. […]
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 […]
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 […]
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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