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UID:1gcgsrpmd4d5dsnq790u69oj88@google.com
CATEGORIES:{lang hu}Algebra szeminárium{/lang}{lang en}Algebra seminar{/lang}
SUMMARY:Dragan Mašulović (University of Novi Sad): Categorical Ramsey Theory
LOCATION:Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:Abstract. Generalizing the classical results of F. P. Ramsey from the late
1920's, the structural Ramsey theory originated at the beginning of 1970s.
We say that a class K of finite structures has the Ramsey property if the f
ollowing holds: for any number k>=2 of colors and all A, B in K such that A
embeds into B there is a C in K such that no matter how we color the copie
s of A in C with k colors, there is a monochromatic copy B' of B in C (that
is, all the copies of A that fall within B' are colored by the same color)
.
Showing that the Ramsey property holds for a class of finite structur
es K can be an extremely challenging task and a slew of sophisticated metho
ds have been proposed in literature. These methods are usually constructive
: given A, B in K and k>=2 they prove the Ramsey property directly by const
ructing a structure C in K with the desired properties. It was Leeb who poi
nted out already in early 1970's that the use of category theory can be qui
te helpful both in the formulation and in the proofs of results pertaining
to structural Ramsey theory. Instead of pursuing the original approach by L
eeb (which has very fruitfully been applied to a wide range of Ramsey probl
ems) we proposed in the last few years a set of new strategies to show that
a class of structures has the Ramsey property.
In this talk we explici
tly put the Ramsey property and the dual Ramsey property in the context of
categories of finite structures. We use elementary category theory to gener
alize some combinatorial results and using the machinery of very basic cate
gory theory provide new combinatorial statements (whose formulations do not
refer to category-theoretic notions) concerning both the Ramsey property a
nd the dual Ramsey property.
DTSTAMP:20240329T001340Z
DTSTART;TZID=Europe/Budapest:20180509T100000
DTEND;TZID=Europe/Budapest:20180509T120000
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