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This week I am at Penn State University, giving this year’s Marker lectures.  My chosen theme for my four lectures here is “recent developments in additive prime number theory”.  My first lecture, “Long arithmetic progressions in primes”, is similar to my AMS lecture on the same topic and so I am not reposting it here.  The second lecture, the notes for which begin after the fold, is on “Linear equations in primes”.  These two lectures focus primarily on work of myself and Ben Green.  The third and fourth lectures, entitled “Small gaps between primes” and “Sieving for almost primes and expander graphs”, will instead be focused on the work of Goldston-Yildirim-Pintz and Bourgain-Gamburd-Sarnak respectively.
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