Reaction networks and toric systems

Abstract: 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).

commutative algebraalgebraic geometry

Audience: researchers in the topic

Max Planck Institute nonlinear algebra seminar online

Series comments: One day before each seminar, an announcement with the Zoom link is mailed to the NASO e-mail list. To receive these e-mails, please sign up on the seminar website www.mis.mpg.de/nlalg/seminars/naso.html.