Abstract. A matroid is the abstraction of the notion of dependence/ind ependence, in particular that of linear independence, algebraic independenc e and graph edge independence. Matroids were introduced in 1936 by H. Whitn ey in his paper ‘On the abstract properties of linear dependence’. A year l ater van der Waerden also did the same (not by the name matroid) in the sec ond edition of his ‘Moderne Algebra’ to unify the treatment of linear and a lgebraic independence. Matroids can be thought of as incident/partial geome tries or indeed as certain lattices. Today matroids play an important role in combinatorics and optimisation.

A central problem in matroid th eory is representability: when is a (finite) matroid isomorphic to a set of vectors under linear independence over some field or division ring? This t urns 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. DTSTAMP:20210724T231756Z DTSTART;TZID=Europe/Budapest:20181114T100000 DTEND;TZID=Europe/Budapest:20181114T120000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR