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CATEGORIES:{lang hu}Algebra szeminárium{/lang}{lang en}Algebra seminar{/lang}
SUMMARY:Vámos Péter: From matroids to equations and back
LOCATION:Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:\nAbstract. A matroid is the abstraction of the notion of dependence/indepe
ndence, in particular that of linear independence, algebraic independence a
nd graph edge independence. Matroids were introduced in 1936 by H. Whitney
in his paper ‘On the abstract properties of linear dependence’. A year late
r van der Waerden also did the same (not by the name matroid) in the second
edition of his ‘Moderne Algebra’ to unify the treatment of linear and alge
braic independence. Matroids can be thought of as incident/partial geometri
es or indeed as certain lattices. Today matroids play an important role in
combinatorics and optimisation.\n\nA central problem in matroid theory is r
epresentability: when is a (finite) matroid isomorphic to a set of vectors
under linear independence over some field or division ring? This turns out
to be a question of solvability of a system of equations and leads to intri
guing interactions between geometry and algebra, and algorithms as well.
DTSTAMP:20220518T192611Z
DTSTART;TZID=Europe/Budapest:20181114T100000
DTEND;TZID=Europe/Budapest:20181114T120000
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