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Workshop

Monotone paths on cross-polytopes

  • Alex Black (UC Davis, Davis, USA)
Live Stream MPI für Mathematik in den Naturwissenschaften Leipzig (Live Stream)

Abstract

In the early 1990s, Billera and Sturmfels introduced monotone path polytopes (MPPs). MPPs encode the combinatorial structure of paths potentially chosen by the simplex method to solve a linear program on a given polytope for a fixed linear functional. In their original paper, they showed that MPPs of simplices and cubes for any generic linear functional are combinatorial cubes and permutahedra respectively. The natural next question to ask is: What are the MPPs of cross-polytopes for generic linear functionals? I will present a complete characterization of MPPs of cross-polytopes for generic linear functionals and show how this result informs our understanding of MPPs of centrally symmetric polytopes. This talk is based on joint work with Jesús De Loera.

Links

conference
4/6/21 4/9/21

(Polytop)ics: Recent advances on polytopes

MPI für Mathematik in den Naturwissenschaften Leipzig Live Stream

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Federico Castillo

Max Planck Institute for Mathematics in the Sciences

Giulia Codenotti

Goethe University Frankfurt

Benjamin Schröter

Royal Institute of Technology (KTH)