From the winner of the Turing Award and the Abel Prize, an introduction to computational
complexity theory, its connections and interactions with mathematics, and its central role in …

Higher order Fourier analysis is a subject that has become very active only recently. This
book serves as an introduction to the field, giving the beginning graduate student in the …

It has been close to ten years since the publication of Green's influential survey Finite field
models in additive combinatorics [28], in which the author championed the use of high …

This collection of open problems has been circulated since 2018 when, encouraged by
Sean Prendiville, I prepared a draft for the Arithmetic Ramsey Theory workshop in …

We present a new approach to constructing pseudorandom generators that fool low-degree
polynomials over finite fields, based on the Gowers norm. Using this approach, we obtain …

In 2007 Terry Tao began a mathematical blog to cover a variety of topics, ranging from his
own research and other recent developments in mathematics, to lecture notes for his …

We prove that the sum of d small-bias generators L: F^ s → F^ n fools degree-d polynomials
in n variables over a field F, for any fixed degree d and field F, including F= F _ 2={0, 1\}. Our …

In GW1 we began an investigation of the following general question. Let L 1,..., L m be a
system of linear forms in d variables on F^ n_p, and let A be a subset of F^ n_p of positive …

We consider the problem of testing if a given function f: F 2 n→ F 2 is close to any degree d
polynomial in n variables, also known as the Reed-Muller testing problem. Alon et al.[1] …

We establish the inverse conjecture for the Gowers norm over finite fields, which asserts
(roughly speaking) that if a bounded function f: V → C on a finite-dimensional vector space V …