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Workshop

Flatness Constant and its Variations

  • Gennadiy Averkov (Brandenburg University of Technology)
E1 05 (Leibniz-Saal)

Abstract

The standard flatness constant is the maximum lattice width among all hollow convex bodies in a given dimension, where hollow means that no lattice points lie in the interior of the body. This value is known exactly in dimensions one and two. There are variations on this constant that arise by restricting the family of the bodies or replacing the hollowness by another condition or replacing the lattice width by other lattice functions. The flatness constant and its variation are useful in integer programming, algebra and algebraic geometry. In this talk I will focus on the role of hollowness in the cutting plane theory for integer optimization problems and highlight the challenge of solving such problems as calculation of the flatness constants or enumeration of special families of lattice polytopes in fixed dimensions.

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Mirke Olschewski

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Thomas Kahle

Otto-von-Guericke-Universität

Bernd Sturmfels

Max-Planck-Institut für Mathematik in den Naturwissenschaften

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