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.