Dr Johannes Hofscheier - Ehrhart Theory of Spanning Lattice Polytopes
Presented by Dr Johannes Hofscheier (University of Nottingham)
A lattice polytope is called spanning if its lattice points affinely span the ambient lattice. This is a relatively mild assumption on lattice polytopes. It is therefore surprising that spanning lattice polytopes share Ehrhart-theoretical properties with much more restrictive classes of lattice polytopes. In the talk, I will explain how the proof of these properties relies on the study of Hilbert functions of sets of points in weighted projective space. If time permits, we conclude with an exciting application of the "spanning property" to obtain universal inequalities in Ehrhart theory.
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