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 Wednesday, 11 Oct. 2023

    Video-Recording for any system with MP4-support

   "SMC prizes for the academic year 2022/2023":

   - Video_pre.mp4  (ca. 55 Mb)

   “SMC-Colloquium lecture by Elisenda Feliu”

   - Video.mp4  (ca. 453 Mb)

 15:15 – 16:55


                  “Positive solutions of parametric polynomial systems

                               and biochemical reaction networks"


                                                  Elisenda Feliu

                                                    (University of Copenhagen)




This talk is centered on the development of tools within the framework of applied algebra for the analysis of mathematical models arising in the study of biochemical reaction networks. In this context, the dynamics of the concentrations of the

chemical species over time are often modelled by a system of parameter-dependent ordinary differential equations, which are typically polynomial or described by

rational functions. Problems such as the determination of the possible number of equilibria for varying parameters, the stability of equilibria, and the existence of bifurcation parameters, can be translated into the study of the solutions to a (huge) system of polynomial equalities and inequalities.


I will start by presenting the challenges within applied algebra of the study of

solutions to polynomial systems of equalities and inequalities, and by introducing

the formalism of the theory of reaction networks. Afterwards I will focus on the problem of counting equilibria by showing recent results that exploit the

connection between the Newton polytope of a multivariate polynomial and the

signs the polynomial attains over the positive orthant. many areas, we will

emphasize the more accessible parts.


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