Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral
tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the …

Recent years have seen a significant rise of interest in max-linear theory and techniques.
Specialised international conferences and seminars or special sessions devoted to max …

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

Triangulations presents the first comprehensive treatment of the theory of secondary
polytopes and related topics. The text discusses the geometric structure behind the …

The quantitative analysis of biological sequence data is based on methods from statistics
coupled with efficient algorithms from computer science. Algebra provides a framework for …

The article surveys structural characterizations of several graph classes defined by distance
properties, which have in part a general algebraic flavor and can be interpreted as subdirect …

This article is based on the Clay Mathematics Senior Scholar Lecture that was delivered by
Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture was the tropical …

We define the tropical analogues of the notions of linear spaces and Plücker coordinates
and study their combinatorics. We introduce tropical analogues of intersection and …

We show that several decision problems originating from max-plus or tropical convexity are
equivalent to zero-sum two player game problems. In particular, we set up an equivalence …

We prove that primal-dual log-barrier interior point methods are not strongly polynomial, by
constructing a family of linear programs with 3r+1 inequalities in dimension 2r for which the …