Combinatorics Seminar 2018

Speaker: Hiroshi Hirai (平井広志), University of Tokyo

Date: Thu, Jul 12, 2018

Time: 15:30 - 16:30

Venue: Middle Meeting Room

Title: Uniform semimodular lattice, valuated matroid, and Euclidean building


In this talk, we present a lattice-theoretic characterization for valuated matroids, which is an extension of the well-known cryptomorphic equivalence between matroids and geometric lattices (=atomistic semimodular lattices). We introduce a class of semimodular lattices, called uniform semimodular lattices, and establish a cryptomorphic equivalence between integer-valued valuated matroids and uniform semimodular lattices. Our result includes a coordinate-free lattice-theoretic characterization of integer points in tropical linear spaces, incorporates the Dress-Terhalle completion process of valuated matroids, and establishes a smooth connection with Euclidean buildings of type A.

The talk is based on the following two papers:

Slides: View slides