Algebra and geometry in the study of enzymatic cascades

DICKENSTEIN, ALICIA

Congreso; Lucia Geometrica; 2019

Universidad de Estocolmo

In recent years, techniques from computational and real algebraic geometry have beensuccessfully used to address mathematical questions in systems biology. Thealgebraic theory of chemical reaction systems aims to understand their dynamicbehavior by taking advantage of the inherent algebraic structure in the kineticequations, and does not need the determination of the parameters a priori,which can be theoretically or practically impossible. From an algebro-geometricperspective, a reaction network gives rise to a family of dynamical systems. Iwill give a gentle introduction to general results based on the networkstructure, in particular related to the important question ofmultistationarity, and I will point out some of the mathematical challengesthat arise from this application.