SEMINAR: Groups and Combinatorics Seminar: Finite vs. infinite fields in matroid representation

Time and place: 11:00 Tuesday 9 February in Weatherburn LT

Speaker: Dillon Mayhew (Victoria University of Wellington)

Title: Finite vs. infinite fields in matroid representation

Abstract: We can think of a matroid as an abstraction of a discrete configuration of points in space. We say that a matroid is representable over a field if those points can be assigned coordinates from the field in a consistent way. There is now a substantial body of work suggesting that matroids representable over finite fields are in some ways well-behaved. Over the last (nearly) two decades, Geelen, Gerards, and Whittle have developed matroid analogues of the Robertson-Seymour theory for graphs. Amongst other results, they have proved Rota's conjecture, and showed that there is no infinite antichain under the minor order for matroids representable over a finite field. On the other hand, the situation for matroids representable over infinite fields seems to be as bad as it possibly can be. This talk will survey all these results, covering joint work with Mike Newman and Geoff Whittle. No knowledge of matroid theory will be assumed.