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 …

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 …

Prime numbers have fascinated mathematicians since the time of Euclid. This book presents
some of our best tools to capture the properties of these fundamental objects, beginning with …

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 …

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 …

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 …

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 …

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 …

Abstract Let g 0,…, gk: N→ D be 1-bounded multiplicative functions, and let h 0,…, hk∈ Z be
shifts. We consider correlation sequences f: N→ Z of the form f (a):= m→∞ 1 log ω m∑ xm/ω …