April 2022 CDT Workshop

Julian Meier, University of Oxford

Interacting-Particle Systems with Elastic Boundaries and Nonlinear SPDEs

We study interacting particle systems on the positive half-line. When we impose an elastic boundary at zero, the particle systems give rise to nonlinear SPDEs with irregular boundaries. We show existence and uniqueness of solutions to these equations. To deal with the nonlinearity we establish a probabilistic representation of solutions and regularity in L2.

Dr Omer Karin, Imperial College London

Mathematical principles of biological regulation

Modern research in the life sciences has developed remarkable methods to measure and manipulate biological systems. We now have detailed knowledge of the molecular interactions inside cells and the way cells communicate with each other. Yet many of the most fundamental questions (such as how do cells choose and maintain their identities? how is development coordinated? why do homeostatic processes fail in disease?) remain elusive, as addressing them requires a good understanding of complex dynamical processes. In this talk, I will present a mathematical approach for tackling these questions, which emphasises the role of control and of emergent properties. We will explore the application of this approach to various questions in biology and biomedicine, and highlight important future directions.