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Workshop

Capturing polytopal symmetries in the edge-graph

  • Martin Winter (TU Chemnitz, Chemnitz, Germany)
Live Stream MPI für Mathematik in den Naturwissenschaften Leipzig (Live Stream)

Abstract

In general dimension the edge-graph of a polytope carries very little information about the polytope itself. For example, the edge-graph can have many more symmetries than the polytope or any realization thereof.

Using techniques from spectral graph theory and convex geometry we show that the edge-graph of every polytope can be colored so that every combinatorial symmetry of the colored edge-graph extends to a geometric symmetry of the polytope.

Up to now, the only proof known of this fact makes use of spectral graph theory and demonstrates the usefulnes of this seemingly unrelated subject in the study of polytopes.

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)