Mike Newman (University of Ottawa)
Excluded minors for real-representable matroids and Ingleton's condition(s)

We consider the question of representability of matroids over the reals. In particular we construct a family of excluded minors for real-representability such that every real-representable matroid is a minor of one of our excluded minors.

This means that characterizing the excluded minors would seem to be very hard. Except that all of our excluded minors can be "explained" by one condition (due to Ingleton).

We will consider actual and possible generalizations of Ingleton's condition, as well as connections with information theory and entropy. We will see what the consequences might be for "characterizing" the excluded minors for real representability.

This is joint work with Dillon Mayhew and Geoff Whittle.