at the

American Institute of Mathematics, San Jose, California

organized by

Mauro Di Nasso, Isaac Goldbring, and Martino Lupini

- Are there specific ways in which nonstandard models can provide further insight into the investigation of the dichotomy between structure and randomness prevalent in many of the arguments in this area, e.g. in the proof of Furstenberg's multiple recurrence theorem?
- Which sumsets configurations can be found in sets of positive density?
- Could such methods be another building block in trying to extend powerful theorems such as Szemeredi's theorem further into the realm of sets with zero density?
- How can iterated nonstandard extensions continue to be used to prove partition regularity of different classes of equations?

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