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Workshop

Flow polytope volume bounds via polynomial capacity

  • Jonathan Leake (TU Berlin, Berlin, Germany)
Live Stream MPI für Mathematik in den Naturwissenschaften Leipzig (Live Stream)

Abstract

Polynomial capacity has been used in the past 20 years to obtain lower bounds on various combinatorial quantities, including the permanent, the mixed discriminant, matchings of a graph, and the intersection of two matroids (to name a few). In joint work with Petter Brändén and Igor Pak, we have recently used capacity to obtain improved lower bounds on the number of contingency tables with given marginals. Contingency tables can be viewed as the lattice points of transportation polytopes and flow polytopes more generally, and so these lower bounds imply volume lower bounds for such polytopes. In this talk, we state these bounds and discuss a few key points of their proofs.

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)