**JOINT MATHEMATICS COLLOQUIUM**

**ICMAT-UAM-UC3M-UCM**

**Positive solutions of parametric
polynomial systems and
biochemical reaction networks**

Elisenda Feliu

(University of Copenhagen)

6 May 2022 - 12:30

Aula Azul, ICMAT

Streaming:

youtu.be/jlbKr63k_is

**In the context of (bio)chemical reaction networks, 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. The
study of the steady states of the system translates then into the study
of the positive solutions to a parametric polynomial system.
In this talk I will start by shortly presenting the formalism of the
theory of reaction networks. Afterwards I will focus on the study of the
parameter region where the relevant parametric system admits at
least two positive solutions (a property termed multistationarity and
of interest in the application). I will show recent results on how to
describe the region and decide whether it is connected. The results
exploit the connection between the Newton polytope of a multivariate
polynomial and the signs the polynomial attains over the positive
orthant.
The results I present arise from several joint works with Conradi,
Kaihnsa, Mincheva, Telek, Yürük, Wiuf and de Wolff.**