Tara Fife:Towards explicit minimal tropical basis for transversal matroids

Abstract: To each circuit of a matroid, we can define a tropical hyperplane. The intersection of these hyperplane yields a tropical linear space, namely the Bergman fan of the matroid. If the tropical hyperplanes associated with a subset, B of the circuit set of M is the same tropical linear space, then B is a tropical basis of M. Tropical basis need not be minimal. Josephine Yu and Debbie Yuster described minimal tropical basis for several classes of matroids and asked for explicit minimal tropical basis for the class of transversal matroids. The talk will begin with an introduction to matroids, including a careful definition of tropical basis. We give explicit minimal tropical basis for two special subclasses of transversal matroids. This is joint work with Yelena Mandelshtan.

Zoom link: https://kth-se.zoom.us/j/65455623260

Zoom meeting ID: 654 5562 3260