Murad Banaji

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  Some combinatorial and algebraic problems arising from the study of chemical reaction networks
  Murad Banaji
  The combinatorial structure of a chemical reaction network (CRN) may determine various behaviours of the associated dynamical systems. From network structure we may gain information about multistationarity, oscillation, bifurcations, persistence, distances between trajectories, orderings of variables, etc. A large number of questions naturally take the form of decision problems (formal languages): can a given network have some particular behaviour? Pursuing results in this area we are led to problems in graph theory, linear and exterior algebra, analysis, and geometry, sometimes of interest beyond their immediate application and intersecting work in other domains. Even where there are elegant characterisations of networks with some property, questions about the complexity of the associated decision problems often remain. I will outline some results and open problems in this area.