Скачать с ютуб Lars Becker: On the Fourier weight of F2 polynomials в хорошем качестве

Lars Becker: On the Fourier weight of F2 polynomials

Given a function f on the hypercube Fn2, define its level k Fourier weight to be the l1-sum of all its Fourier coefficients associated to sets with k elements. If f is a polynomial of degree d, then how large can its level k Fourier weight be? This question was posed by Chattopadhyay, Hatami, Hosseini and Lovett, motivated by applications to pseudorandom generators. They conjecture an upper bound exponential in k and polynomial in d. We present a proof of this conjecture for level 1 and polynomials of any degree, due to the above listed authors and Tal. Further, we give a proof for degree 2 polynomials and any level k, which is joint work with Alexander Volberg.