|Location:||MSRI: Simons Auditorium|
A lattice polytope is called spanning (or primitive) if its lattice points affinely span the ambient lattice. This property can be translated to a natural algebraic property of the Ehrhart ring of the polytope.
In this talk, I will present recent joint work with Johannes Hofscheier and Benjamin Nill, where we use methods from commutative algebra and algebraic geometry to obtain new inequalities for the h^*-vector.
This extends our previous work on the absence of inner zeros in the h^*-vector, as well as Hibi's inequality for polytopes with inner lattice points.