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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)
.\nShowing that the Ramsey property holds for a class of finite structures
K can be an extremely challenging task and a slew of sophisticated methods
have been proposed in literature. These methods are usually constructive: g
iven A, B in K and k>=2 they prove the Ramsey property directly by construc
ting a structure C in K with the desired properties. It was Leeb who pointe
d out already in early 1970's that the use of category theory can be quite
helpful both in the formulation and in the proofs of results pertaining to
structural Ramsey theory. Instead of pursuing the original approach by Leeb
(which has very fruitfully been applied to a wide range of Ramsey problems
) we proposed in the last few years a set of new strategies to show that a
class of structures has the Ramsey property.\nIn this talk we explicitly pu
t the Ramsey property and the dual Ramsey property in the context of catego
ries of finite structures. We use elementary category theory to generalize
some combinatorial results and using the machinery of very basic category t
heory provide new combinatorial statements (whose formulations do not refer
to category-theoretic notions) concerning both the Ramsey property and the
dual Ramsey property.
DTSTAMP:20200604T110615Z
DTSTART;TZID=Europe/Budapest:20180509T100000
DTEND;TZID=Europe/Budapest:20180509T120000
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