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'Hollow' Lattice PolytopesAlgebra & Discrete Mathematics
|Speaker: ||Benjamin Nill, MSRI|
|Location: ||2112 MSB|
|Start time: ||Fri, Nov 20 2009, 4:10PM|
In the geometry of numbers one of the main objects of study are
lattice-point-free convex bodies. In this talk I will give a survey of
conjectures and results on the corresponding objects in the world of lattice
polytopes: lattice polytopes without interior lattice points.
It turns out that there is a nice invariant in Ehrhart theory,
called the codegree, which measures the 'hollowness' of these lattice
polytopes. In joint work with Christian Haase and Sam Payne, we could
prove a structure theorem on lattice polytopes with large codegree,
which yields a new finiteness result on Ehrhart polynomials.
If time allows, I will also present related work in progress with
Sandra Di Rocco and Christian Haase.