Seminario Álgebra Geometría Algebraica y Aritmética
The geometry of steady state varieties in Chemical Reaction Networks
Ponente: Beatriz Pascual Escudero (UPM)Fecha: miércoles 26 de marzo de 2025 - 13:45Lugar: Aula 420, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
In Biochemistry, Ecology, Epidemiology and some other fields, Reaction Networks represent interactions among species, such as proteins in some cellular process. The evolution of the concentrations of these species in the process can be described using autonomous ODE systems. These equations can involve many parameters, that in general are unknown or experimentally measured. Assuming some types of kinetics, such as mass action, these equations are polynomials.
When we study these systems' steady states in the mass-action case, we study the set of positive points of an affine algebraic variety and, as we will see, here is where Algebraic Geometry and Computational Algebra can help: even with so many variables involved and so many unknown parameters, the network and kinetics determine the structure of the polynomials and therefore speak about certain (important) aspects of the geometry of the variety. This also makes it possible to understand some properties of the dynamical system and sometimes of the network, even without knowing the parameters.
We will present mass-action systems, analyze their structure, and show the consequences of this structure for the (generic) geometry of steady state varieties, as well as for the dynamics of a given network.
