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Polytopes, successive minima, and the logarithmic Minkowski problem

Algebra & Discrete Mathematics

Speaker: Martin Henk, U. Magdeburg, Germany
Location: 1147 MSB
Start time: Mon, Oct 27 2014, 1:10PM

We discuss several extensions/variations of Minkowski's classical second theorem on successive minima. Among others, we present a (possible) "lattice point generalization" of this theorem which relates to Ehrhart theory of lattice polytopes and to the logarithmic Minkowski problem, a central problem in modern convex geometry. Most of the given results are part of joint works with Karoly J. Boroczky, Matthias Henze & Maria Hernandez Cifre, and Eva Linke.