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                * Princeton Discrete Math Seminar *
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Speaker: Ashwin Sah (MIT)

Thursday 2nd November, 3:00 in Fine Hall 224.

Title: Effective bounds for Roth's theorem with shifted square common difference

Let S be a subset of 1,…,N avoiding the nontrivial progressions x, x+y^2-1,
x+2(y^2-1). We prove that |S|<N/loglog…log(N), where we have a fixed constant
number of logarithms. This answers a question of Green, and is the first 
effective polynomial Szemerédi result over the integers where the polynomials 
involved are not homogeneous of the same degree and the underlying pattern has 
linear complexity. Joint work with Sarah Peluse and Mehtaab Sawhney.

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