Combinatorics Seminar: On Equivalence of Polynomial Conjectures in Additive Combinatorics

Shachar Lovett (Weizmann Institute)
Wednesday, 6.1.2010, 13:30
Amado 719

We will discuss two important conjectures in additive combinatorics. The first one is the polynomial Freiman-Rusza conjecture, which relates to the structure of sets with small doubling. The second is the inverse Gowers conjecture for $U^3$, which relates to functions which locally look like quadratics. In both conjectures a weak form, with exponential decay of parameters is known, and a strong form with only a polynomial decay of parameters is conjectured.

We will show that the two conjectures are in fact equivalent. This was also discovered independently by Green and Tao

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