Mathematical models in biology and population dynamics

Complex systems in nature and applied sciences often consist of multiple interacting components and occur across multiple temporal and spatial scales. They are often described by systems of ordinary/stochastic/partial differential equations. A mathematical study, including analytical analysis and numerical simulations, of such equations is pivotal for the understanding and control of the underlying system. However, they are challenging problems because of the complexity and nonlinearity of the systems.
The aim of this PhD project is to develop mathematical methods for analysing complex systems arising from biology, population dynamics, as well as statistical physics. Examples include the Langevin dynamics, the generalized Langevin dynamics, and the relativistic Langevin dynamics. We will show the well-posedness of the mathematical equations, study their multiscale and long-time behavour as well as develop numerical computational methods. We will employ techniques from different areas of mathematics such as probability theory, stochastic processes, and partial differential equations.