Tommaso Lorenzi

Politecnico di Torino, Turin, Italy

Mathematical models formulated as partial differential equations (PDEs) have played an increasingly prominent role in different branches of biology as tools to consolidate experimental data, dissect out biological processes, provide a formal basis for the formulation of novel hypotheses, and inform new experiments that may help identify unexplored research streams. As such, these models have been highly influential in the development of mathematical biology into a research area in its own right within the field of applied mathematics. In this talk, I will give a brief overview of PDE approaches for modelling spatiotemporal and evolutionary dynamics in biological systems. I will first set the scene through a short review of some classic PDE models in mathematical biology and their possible extensions. I will then proceed with a tutorial-style presentation on key qualitative properties of the solutions to such models and mathematical methods that have been developed to study these properties.