Reaction networks and toric systems

Mass-action networks (edge labelled directed graphs) model cascades of chemical reactions (e.g. used by biological systems for adapting to the environment). From the assumption of mass-action kinetics, a mass-action network gives rise to a polynomial dynamical system. In this large class of polynomial systems, the intuition from Chemistry and Algebraic Geometry feed themselves, giving exciting new results. For example, we will discuss complex balanced mass-action networks, which have a natural chemical interpretation and (conjecturally) completely determines the dynamics of the associated systems (called toric dynamical systems). We will introduce "disguised toric systems", which exploit this relationship the other way around: given a dynamical system, can we build a complex balanced mass-action network for it?

(Joint work with Gheorghe Craciun and Miruna-Ştefana Sorea).