On the Fourier Weight of F2 Polynomials

Explore the intricacies of Fourier weight in F2 polynomials through this 36-minute lecture by Lars Becker at the Hausdorff Center for Mathematics. Delve into the concept of level k Fourier weight for functions on the hypercube Fn2, and examine the upper bounds for polynomials of varying degrees. Learn about the conjecture proposed by Chattopadhyay, Hatami, Hosseini, and Lovett, which suggests an upper bound exponential in k and polynomial in d. Discover the proof for level 1 and polynomials of any degree, as well as the proof for degree 2 polynomials and any level k, the latter being a joint work with Alexander Volberg. Gain insights into the applications of this research in the field of pseudorandom generators.

Lars Becker: On the Fourier weight of F2 polynomials