The Catholic University Department of Mathematics hosts a weekly seminar in Functional Analysis and Related Areas. Attendance is open to all interested members of the mathematics community, including students and faculty from other colleges and universities. See below for an abstract of the upcoming presentation.
SEMINAR IN FUNCTIONAL ANALYSIS
AND RELATED AREAS
Wednesday, September 29, 2022
SPEAKER: Professor Neil Hindman
TITLE: Pairwise sums and products in ℝ+
(Joint research with Maria-Romina Ivan and Imre Leaderwork with Vitaly Bergelson)
FS, FP, PS, and PP stand for finite sums, finite products, pairwise sums and pairwise products respectively, all without repetition. Sometime shortly after the big bang it was shown that if a semigroup (S, ·) is finitely colored, there are a sequence ⟨xn⟩1≤ n < ∞ and a color class which contains FP(⟨xn⟩1≤ n < ∞).
In 1999, Bergelson, Hindman, and Leader showed that if the real interval (0, 1) is finitely colored and each color class is measurable or each color class has the property of Baire, then there are a sequence ⟨xn⟩1≤ n < ∞ and a color class which contains FS(⟨xn⟩1≤ n < ∞) FP(⟨xn⟩1≤ n < ∞).
The first of our results that I will discuss shows that there is a finite coloring of the positive reals such that each color class is either open or countable (so is measurable and has the property of Baire) and if ⟨xn⟩1≤ n < ∞ is a sequence with PS(⟨xn⟩1≤ n < ∞) PP(⟨xn⟩1≤ n < ∞) monochromatic, then either xn approaches zero or xn approaches infinity.
This presentation will be given via Zoom. The corresponding link will be sent to everyone in advance.
ORGANIZERS: V. Bogdan (Catholic University), P. Kainen (Georgetown University), R. Kalpathy (Catholic University), and A. Levin (Catholic University).