The birational geometry of matroids

Abstract

In this talk, I will consider isomorphisms of Bergman fans of matroids. Motivated by algebraic geometry, these isomorphisms can be considered as matroid analogs of birational maps. I will introduce Cremona automorphisms of the coarsest fan structure. These produce a class of automorphisms which do not come from automorphisms of the underlying matroid. I will then explain that the automorphism group of the coarse fan structure is generated by matroid automorphisms and Cremona maps when the fan is 2-dimensional and also for modularly complemented matroids. I will assume no background on matroid theory for this talk. This is based on joint work with Annette Werner

About the speaker

Kristin Shaw is a professor of mathematics at the University of Oslo (UiO). He mainly study connections between combinatorics and algebraic geometry over the real and complex numbers. He is leading the research group on Algebraic and Topological Cycles in Tropical and Complex Geometries funded by the BFS.

Prior to coming to the University of Oslo, he was a postdoc at the Max Planck Institute Leipzig, the Technical University of Berlin, and the University of Toronto. He also spent time as a postdoc at the Fields’ Institute semester in Combinatorial Algebraic Geometry.