Alessandro Vegnuti:
Archimedean classes of hypernaturals, and their use in ART
Time and place
Tuesday, 28.10.25, 14:30-16:00, Seminarraum 404
Abstract
Arithmetic Ramsey Theory (ART) studies what kind of arithmetic configurations we cannot
avoid taking a finite partition of the naturals: arithmetic progressions, large sets with all possible
sums of their elements, solutions to certain polynomials are just some examples of these configurations
(usually called Partition Regular, PR).
How to deal with such problems? In the last years, ideas coming from nonstandard analysis -
and linked with ultrafilter algebra - have provided a natural framework to study Ramsey-theoretic
questions.
In this talk, we will present a new tool to prove that certain polynomials are not PR: by adopting
the nonstandard point of view, we will show how the notion of Archimedean classes of hypernaturals
can easily produce negative results in ART.
This is a joint work with Lorenzo Luperi Baglini.