# Beatriz Pascual Escudero: Using Algebraic Geometry to detect robustness in Reaction Networks

**Time: **
Tue 2021-02-23 11.15

**Lecturer: **
Beatriz Pascual Escudero, Universidad Carlos III de Madrid

**Location: **
Zoom, meeting ID: 625 8662 8413

### Abstract

An interesting feature of some biological systems is their capacity to preserve certain features against changes in the environmental conditions. In particular, we are concerned with the preservation of the concentration of specific species interacting in a system, motivated by examples in Reaction Networks: a biological system has absolute concentration robustness (ACR) for some molecular species if the concentration of this species does not vary among the different equilibria that the network admits. In particular, this concentration is independent of the initial conditions. While some classes of networks with ACR have been described, as well as some techniques to check ACR for a given network, finding networks with this property is a difficult task in general.

Motivated by this problem, we will explore local and global notions of robustness on the set of (real positive) solutions of a system of polynomial equations. The goal is to provide a practical test on necessary conditions for ACR, using algebraic-geometric techniques. This is based on joint work with E. Feliu.