Title: Hilbert Schemes and Newton-Okounkov Bodies

Abstract: Hilbert schemes of points in the plane parametrize finite, closed subschemes of C^2 with a fixed length. In this talk, I will explain how to compute the Newton-Okounkov bodies of these Hilbert schemes, which are certain unbounded polyhedra encoding geometric information about the Hilbert schemes. Finally, I will share what is known for Hilbert schemes of points on complete toric surfaces.