Event Details

A mathematics talk for a general audience, given by a member of the School of Mathematical Sciences, Dr. Murad Banaji.

Title: From network dynamical systems to algebra

Abstract: Dynamical systems with network structure arise across the sciences, especially in biology and chemistry. Subpopulations, or genes, or chemical species interact with each other in complicated ways, and somehow, from these interactions, a wide variety of behaviours emerge. Studying such systems to decode their dynamics can give rise to interesting problems in algebra. One class of problems arises when we study bifurcations: sudden qualitative changes in the behaviour of a system as we vary some parameters. When deciding if a bifurcation takes place, we often end up facing some system of algebraic equations. Feasibility of the system, or the cardinality of the solution set, may tell us about the occurrence or impossibility of some bifurcation. But these systems of equations inherit combinatorial properties from the networks, and this can open up new approaches to analysing the equations. Practically speaking, we can sometimes guarantee or rule out certain behaviours in dynamical systems based on their network structure alone. I will give a gentle introduction to some work on these themes, with plenty of pictures and examples.