Milena Hering (UC Berkeley):   The caterpillar polytope and its relatives

I will talk about a family of toric varieties that arise as degenerations of the geometric invariant theory quotient of n points on the sphere. I will show that these toric varieties exhibit some very nice properties -- they are Frobenius split, and their homogeneous coordinate rings admit a presentation whose ideal admits a quadratic Gröbner basis. I will explain how these results apply to the original ring of invariants. I am reporting on joint work with Benjamin Howard.