David Fernández-Bretón: Algebraic Ramsey-theoretic results with small monochromatic sets

BIU seminar in Set Theory

November 5, 2018

Speaker: David J. Fernández Bretón (KGRC)

Title: Algebraic Ramsey-theoretic results with small monochromatic sets

Abstract: We will explore some (recent and not so recent; some positive,
some negative) Ramsey-type results (each of which is due to some subset
of the set {Komj\’ath, Hindman, Leader, H.S. Lee, P. Russell, Shelah, D.
Soukup, Strauss, Rinot, Vidnyánszky, myself}) where abelian groups are
coloured, and one attempts to obtain monochromatic sets defined in terms
of the group structure. We will focus specifically on two families of
very recent results: the first one concerns colouring groups with
uncountably many colours, attempting to obtain finite monochromatic
FS-sets; the second one concerns colouring groups (most of the time, our
group of interest is the real line $\mathbb R$ with its usual addition)
with finitely many colours, attempting to obtain countably infinite
monochromatic sumsets.

Leave a Reply

Your email address will not be published. Required fields are marked *

Time limit is exhausted. Please reload CAPTCHA.

This site uses Akismet to reduce spam. Learn how your comment data is processed.