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                * Princeton Discrete Math Seminar *
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Speaker: James Leng (UCLA)

Thursday 17th April, 3:00 in Fine Hall 224.

Title: Szemerédi’s theorem, primes, and nilsequences.


Let r_k(N) be the largest subset of [N] = {1,...,N} with no k-term 
arithmetic progression. Szemerédi’s theorem states that r_k(N) = o_k(N). 
We will go over the proof that achieves the best known upper bounds
for r_k(N) for general k. We will discuss how the mathematics behind the
proof relates to counting primes along linear forms and the distribution of
orbits on G/Gamma with G nilpotent and Gamma discrete and cocompact.
This is (partly) based on joint work with Ashwin Sah and Mehtaab Sawhney.

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