Wolfe Lecture: Patterns in primes and dynamics on nilmanifolds
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A classical theorem of Dirichlet establishes the existence of infinitely many primes in arithmetic progressions, so long as there are no local obstructions. In 2006 Green and Tao set up a programme for proving a vast generalization of this theorem. They conjectured a relation between the existence of linear patterns in primes and dynamics on nilmanifolds. In joint work with Green and Tao we completed the final step of this programme.
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