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
This is the second thread for the Polymath8b project to obtain new bounds for the quantity either for small values of (in particular ) or asymptotically as . The previous thread may be found here. The currently best known bounds on are: (Maynard) . (Polymath8b, tentative) . (Polymath8b, tentative) for sufficiently large . (Maynard) Assuming […]
For each natural number , let denote the quantity where denotes the prime. In other words, is the least quantity such that there are infinitely many intervals of length that contain or more primes. Thus, for instance, the twin prime conjecture is equivalent to the assertion that , and the prime tuples conjecture would imply […]
It’s time to (somewhat belatedly) roll over the previous thread on writing the first paper from the Polymath8 project, as this thread is overflowing with comments. We are getting near the end of writing this large (173 pages!) paper, establishing a bound of 4,680 on the gap between primes, with only a few sections left […]
The classical foundations of probability theory (discussed for instance in this previous blog post) is founded on the notion of a probability space – a space (the sample space) equipped with a -algebra (the event space), together with a countably additive probability measure that assigns a real number in the interval to each event. One […]
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