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                * Princeton Discrete Math Seminar *
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Date: Thursday 1st May, 4:30 in Fine Hall 224.
 
Speaker: Jacob Fox (MIT)

Title: The Green-Tao Theorem and a Relative Szemerédi Theorem

Abstract: The celebrated Green-Tao theorem states that there are
arbitrarily long arithmetic progressions in the primes. In this talk, I
will explain the ideas of the proof and recent joint work with David Conlon
and Yufei Zhao simplifying the proof. The main new ingredient in the proof
of the Green-Tao theorem is a relative Szemerédi theorem, which says that
any subset of a pseudorandom set of integers of positive relative density
contains long arithmetic progressions. Our main advance is a simple proof
of a strengthening of the relative Szemerédi theorem, showing that a much
weaker pseudorandomness condition is sufficient. The key component in our
proof is an extension of the regularity method to sparse hypergraphs.

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Next week: summer break

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