Elisenda Feliu (Copenhagen) Algebra approaches in the study of reaction networks

Abstract: Biochemical reaction networks describe how interacting chemical species evolve over time. Their dynamics are commonly modelled by systems of ordinary differential equations whose right-hand sides are polynomial or rational functions. Fundamental questions include whether a network can admit multiple equilibria, whether these equilibria are stable, and how qualitative changes in the dynamics (bifurcations) can occur as parameters vary. Many of these questions can be reformulated as problems about the solutions of systems of polynomial equations and inequalities, making them amenable to methods from algebra and real algebraic geometry. This talk will first introduce the mathematical framework of reaction networks and relevant questions. Afterwards I will give examples of how algebraic techniques can be used to study several aspects of their dynamics, and at the same how advancement in this field has contributed to general results for general polynomial systems.\n\nhttps://indico.math.cnrs.fr/event/16474/