Title: Hilbert Schemes and Newton-Okounkov Bodies
Abstract: The Hilbert scheme of n points in the affine plane parametrizes finite, length n subschemes of the plane. Equivalently, it parametrizes ideals in the polynomial ring C[x,y] with colength n. In this talk, I will discuss the “Newton-Okounkov bodies” of these Hilbert schemes, which are certain unbounded polyhedra that encode some aspects of their geometry. If time permits, I will also share what is known about the Newton-Okounkov bodies of Hilbert schemes of points on other surfaces.
