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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)
Abstract:
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.