"An Optimal Inverse Theorem"
Guy Moshkovitz (CUNY)
Monday, March 29th 2021, 2-3pm
Abstract:
The rank and analytic rank of a (multilinear) polynomial measure algebraic structure and bias, respectively. We prove that they are equivalent up to a constant, over any large enough finite field (independently of the number of variables). The proof constructs rational maps computing a rank decomposition for successive derivatives, on a carefully chosen subset of a kernel variety associated with the polynomial. Proving the equivalence between these two quantities is the main question in the "bias implies low rank" line of work in higher-order Fourier analysis, and was reiterated by multiple authors.
Joint work with Alex Cohen.