The steady-state degree and mixed volume of a chemical reaction network

Student Algebraic Geometry Seminar
Friday, March 26, 2021 - 9:00am for 1 hour (actually 50 minutes)
Cvetelina Hill – Georgia Tech –
Marc Harkonen
Chemical reaction networks (CRNs), under the assumption of mass-action kinetics, are deterministic polynomial systems commonly used in systems biology. The steady-state of a CRN is the number of complex steady-states (solutions to the polynomial system), which is a measure of the algebraic complexity of solving the steady-state system. In general, the steady-state degree may be difficult to compute. Using three case studies of infinite families of networks, each generated by joining smaller networks to create larger ones, we give an upper bound to the steady-state degree of a CRN by utilizing the underlying polyhedral geometry associated with the corresponding system. In this talk I will give an overview of the necessary background for CRNs and the associated polyhedral geometry, and I will discuss the results on one of the case studies through examples.