From chemical reaction networks to algebraic and polyhedral geometry -- and back again

TL;DR

This chapter reviews Bernd Sturmfels's influential work on applying algebraic and combinatorial methods to analyze chemical reaction networks, focusing on steady states and the global attractor conjecture.

Contribution

It highlights Sturmfels's novel integration of algebraic geometry and combinatorics into the study of chemical reaction networks, advancing understanding of steady states and network dynamics.

Findings

Analysis of steady-state varieties

Counting steady states techniques

Insights into the global attractor conjecture

Abstract

This is a chapter for a book in honor of Bernd Sturmfels and his contributions. We describe the contributions by Bernd Sturmfels and his collaborators in harnessing algebraic and combinatorial methods for analyzing chemical reaction networks. Topics explored include the steady-state variety, counting steady states, and the global attractor conjecture. We also recount some personal stories that highlight Sturmfels's long-lasting impact on this research area.