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Vámos Péter: From matroids to equations and back

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Wednesday, 14. November 2018, 10:00 - 12:00

Abstract. A matroid is the abstraction of the notion of dependence/independence, in particular that of linear independence, algebraic independence and graph edge independence. Matroids were introduced in 1936 by H. Whitney in his paper ‘On the abstract properties of linear dependence’. A year later 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 algebraic independence. Matroids can be thought of as incident/partial geometries or indeed as certain lattices. Today matroids play an important role in combinatorics and optimisation.

A central problem in matroid theory is representability: 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 intriguing interactions between geometry and algebra, and algorithms as well.
Location : Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged


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