Theory and applications of lattice point methods for binomial ideals

TL;DR

This survey explores lattice point methods for binomial ideals, covering geometric combinatorics and three applications in hypergeometric systems, game theory, and chemical dynamics, with accessible explanations and open problems.

Contribution

It provides a comprehensive overview of lattice point techniques for binomial ideals and connects them to diverse applications beyond algebra.

Findings

Detailed treatment of binomial primary decomposition

Applications to hypergeometric systems, game theory, and chemical dynamics

Includes examples, open problems, and elementary background

Abstract

This survey of methods surrounding lattice point methods for binomial ideals begins with a leisurely treatment of the geometric combinatorics of binomial primary decomposition. It then proceeds to three independent applications whose motivations come from outside of commutative algebra: hypergeometric systems, combinatorial game theory, and chemical dynamics. The exposition is aimed at students and researchers in algebra; it includes many examples, open problems, and elementary introductions to the motivations and background from outside of algebra.