We prove the inverse conjecture for the Gowers U s+ 1 N-norm for all s≥ 1; this is new for
s≥ 4. More precisely, we establish that if f: N→− 1, 1 is a function with …

A theorem of Leibman asserts that a polynomial orbit (g (n) Γ) n∈ ℤ on a nilmanifold G/Γ is
always equidistributed in a union of closed subnilmanifolds of G/Γ. In this paper we give a …

We show that the Möbius function μ (n) is strongly asymptotically orthogonal to any
polynomial nilsequence (F (g (n) Γ)) n∈ ℕ. Here, G is a simply-connected nilpotent Lie …

On the Bogolyubov--Ruzsa lemma Page 1 ANALYSIS & PDE mathematical sciences
publishers Volume 5 No. 3 2012 TOM SANDERS ON THE BOGOLYUBOV–RUZSA LEMMA …

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 …

Nilsystems play a key role in the structure theory of measure preserving systems, arising as
the natural objects that describe the behavior of multiple ergodic averages. This book is a …

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 …

We establish the existence of infinitely many polynomial progressions in the primes; more
precisely, given any integer-valued polynomials P 1,…, P k∈ Z m in one unknown m with P …

The Möbius disjointness conjecture of Sarnak states that the Möbius function does not
correlate with any bounded sequence of complex numbers arising from a topological …

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 …