Topological reaction-diffusion networks

I will describe a class of reaction-diffusion equations that appear in biology and closely resemble dynamical systems of Hamiltonian form. As such, their mathematical properties can be studied using the framework of symplectic geometry, and biologically inspired questions (such as the existence of periodic orbits, Turing instability, synchronisation etc) can be reformulated as purely topological problems. The talk will be at a level suitable for those interested in the wider applications of complex network theory and assumes no previous exposure to topology or symplectic geometry.