Nonstandard methods in combinatorial number theory
August 14 to August 18, 2017
American Institute of Mathematics,
San Jose, California
Mauro Di Nasso,
and Martino Lupini
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
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?
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: