Colloquium (Math) - Matteo Smerlak

Speaker: Matteo Smerlak (Max Planck Institute for Mathematics in the Sciences, Leipzig)

"Evolutionary landscapes and retrospective processes"

Many systems across the sciences evolve through the interaction of multiplicative growth and diffusive transport. In the presence of disorder, these opposing forces can generate localized structures and bursty dynamics, a phenomenon known as "intermittency" in non-equilibrium physics and as "punctuated equilibrium" in evolutionary theory. This behaviour is difficult to forecast; in particular there is no general principle to locate the regions where the system will settle, how long it will stay there, or where it will jump next. In this talk I will introduce a Markovian representation of growth-transport dynamics that closes these gaps. This retrospective view of evolution unifies the concepts of linear intermittency and metastability, and provides a generally applicable method to reduce, and predict, the dynamics of disordered linear systems. Applications range from Zeld'dovich's parabolic Anderson model to Eigen's quasispecies model of molecular evolution.