#
Additive combinatorics and its applications

August 20 to August 24, 2018
at the

American Institute of Mathematics,
San Jose, California

organized by

Ben Green,
Shachar Lovett,
Olof Sisask,
and Madhur Tulsiani

## Original Announcement

This workshop will be devoted to additive
combinatorics and its applications in mathematics and computer science. One of
the chief concerns of additive combinatorics is the classification of sets or
functions that are only approximately algebraically structured, and results in
this direction have turned out to be useful in diverse parts of mathematics and
theoretical computer science, for instance in finding linear structures in
various sets of integers and in property testing. Conversely, the need for
stronger results to cater for applications has driven the development of
additive combinatorics. The aim of this workshop is to gather researchers from
all sides of these developments in order to tackle some of the area's
fundamental problems.
The main topics for the workshop are:

- New applications for additive combinatorics in number theory and algorithm
design and analysis
- The polynomial Freiman-Ruzsa conjecture, one of the central open problems in
additive combinatorics
- The new polynomial method of Croot-Lev-Pach and Ellenberg-Gijswijt;
Understanding its power and limitations, and how to overcome them.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

Workshop Videos