About:

Additive combinatorics is in an astonishingly active period of development, in the UK and worldwide. There have been so many major advances in the past decade that we cannot list them all, but they include: quasipolynomial upper bounds in Roth's theorem, a resolution of the cap-set problem, effective inverse theorems for Gowers uniformity norms, a power-saving bound for difference sets avoiding shifted primes, polynomial bounds in the true complexity problem for linear systems, the resolution of the Erdos sumset conjecture, lower-bounds on off-diagonal van der Waerden numbers W(3,k), effective bounds for sets lacking shifted polynomial patterns of distinct degrees, the introduction of stable arithmetic regularity, and continued progress on the Erdos-Szemeredi sum-product problem.

The aim of this workshop was to gather together experts from different subfields of additive combinatorics, to foster in-depth discussion of the legion of recent advances, and to explore avenues for future research. Specific places were reserved for PhD students, to develop and encourage the next generation of researchers. A volume of conference proceedings will be compiled, including 5 expository plenary talks, along with a list of open problems.