Ollie Clarke

Combinatorial Mutations and Block Diagonal Polytopes

Matching fields were introduced by Sturmfels and Zelevinsky to study certain Newton polytopes and more recently have been shown to give rise to toric degenerations of various families of varieties. Whenever a matching field gives rise to a toric degeneration of the Grassmannian, the associated polytope of the toric variety coincides with the matching field polytope. In this talk I will introduce combinatorial mutations of matching field polytopes. We will explore properties of polytopes which are preserved by mutation, in particular the property of giving rise to a toric degeneration is preserved by mutations. This gives us an easy way to generate new families of toric degenerations of the Grassmannian from old.