Nonstandard methods in combinatorial number theory

August 14 to August 18, 2017

at the

American Institute of Mathematics, San Jose, California

organized by

Mauro Di Nasso, Isaac Goldbring, and Martino Lupini

Original Announcement

This workshop hopes to further develop the use of nonstandard methods in combinatorial number theory and Ramsey theory. For example, recently nonstandard methods have proven useful in problems about configurations of sumsets in sets of positive density as well as partition regularity of equations. Our aim is to continue to explore these and other directions leading to a greater understanding of the role that nonstandard methods could play in this area of combinatorics. Examples of specific questions include:

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Weighted real Egyptian numbers
by  Melvyn B. Nathanson
On supra-SIM sets of natural numbers
by  Isaac Goldbring and Steven Leth
A proof of the Erdos sumset conjecture
by  Joel Moreira, Florian Karl Richter, and Donald Robertson
Abstract densities and ideals of sets
by  Mauro Di Nasso and Renling Jin
Szemeredi's proof of Szemeredi's theorem
by  Terence Tao