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SEMINARS
Uniform semimodular lattice, valuated matroid, and Euclidean building
时间  Datetime
2018-07-12 15:30 — 16:30 
地点  Venue
Middle Lecture Room
报告人  Speaker
Hiroshi Hirai (平井広志)
单位  Affiliation
University of Tokyo
邀请人  Host
Yaokun Wu
报告摘要  Abstract

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: