Expander graphs are highly connected sparse finite graphs. They play an important role in
computer science as basic building blocks for network constructions, error correcting codes …

AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM Page 1 Proceedings of the
Edinburgh Mathematical Society (2008) 51, 73–153 c DOI:10.1017/S0013091505000325 …

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 …

" There are many bits and pieces of folklore in mathematics that are passed down from
advisor to student, or from collaborator to collaborator, but which are too fuzzy and non …

THE LOGARITHMICALLY AVERAGED CHOWLA AND ELLIOTT CONJECTURES FOR TWO-POINT
CORRELATIONS Page 1 Forum of Mathematics, Pi (2016), Vol. 4, e8, 36 pages doi:10.1017/fmp.2016.6 …

= o (HX) provided that H→∞ arbitrarily slowly with X→∞(and H≤ X). Note that the k= 2 case
of Chowla's conjecture is equivalent to the above asymptotic holding in the case that H is …

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 …

Let O be an orbit in ℤ n of a finitely generated subgroup Λ of GL n (ℤ) whose Zariski closure
Zcl (Λ) is suitably large (eg isomorphic to SL 2). We develop a Brun combinatorial sieve for …

Let $ p_n $ denote the $ n $ th prime. We prove that\[\max _ {p_ {n}\leqslant X}(p_ {n+ 1}-
p_n)\gg\frac {\log X\log\log X\log\log\log\log X}{\log\log\log X}\] for sufficiently large $ X …

We consider the following basic question: to what extent are standard secret sharing
schemes and protocols for secure multiparty computation that build on them resilient to …