Given a graph H, the Ramsey number r (H) is the smallest natural number N such that any
two-colouring of the edges of KN contains a monochromatic copy of H. The existence of …

Additive combinatorics is the theory of counting additive structures in sets. This theory has
seen exciting developments and dramatic changes in direction in recent years thanks to its …

Tim Gowers is not your typical blogger. A mathematician at Cambridge University, Gowers is
a recipient of the highest honor in mathematics, the Fields Medal, often called the Nobel …

Recently, it became apparent that a large number of the most interesting structures and
phenomena of the world can be described by networks. To develop a mathematical theory of …

Boosting is a general method for improving the accuracy of learning algorithms. We use
boosting to construct improved privacy-pre serving synopses of an input database. These …

In this volume we have endeavored to provide a middle ground-hopefully even a bridge-
between" theory" and" experiment" in the matter of prime numbers. Of course, we speak of …

Interactive querying of a database degrades the privacy level. In this paper we answer the
fundamental question of characterizing the level of privacy degradation as a function of the …

Many mathematicians are aware of some of the dramatic interactions between ergodic
theory and other parts of the subject, notably Ramsey theory, infinite combinatorics, and …

Differential privacy is a theoretical framework for ensuring the privacy of individual-level data
when performing statistical analysis of privacy-sensitive datasets. This tutorial provides an …

[I] ntuition comes to us much earlier and with much less outside influence than formal
arguments which we cannot really understand unless we have reached a relatively high …