Algebra Seminar - "Ehrhart Theory: When Hilbert functions meet lattice polytopes", Johannes Hofscheier
Title: Ehrhart Theory: When Hilbert functions meet lattice polytopes
Abstract: In this talk we will give an introduction to Ehrhart Theory with a view toward Hilbert functions. A lattice polytope is the convex hull of finitely many points in real Euclidean space with integer coordinates. They play an important role in many parts of mathematics, e.g., in algebraic geometry, in optimization theory, in discrete mathematics and in the geometry of numbers. To a lattice polytope one associates a ring whose Hilbert function is the Ehrhart function of the polytope. It is a challenging and fascinating open problem how the geometry of the polytope affects the shape of the Hilbert function. We will give an overview of the major unsolved problems in this field and complete our talk with a recent result yielding such a connection. This is joint work with Lukas Katthän and Benjamin Nill.