Foundations. Optimal control with ODE/PDE constraints, mathematical control theory, convex optimisation. High-dimensional approximation and learning, numerical methods for Hamilton-Jacobi-Bellman and related PDEs. Optimal transport, mean-field control/games. Nonlinear model reduction.

Applications. Scientific Machine Learning, data-driven modelling \& control. Agent-based models: nonlocal PDES, collective behaviour, global optimisation. Nonlinear control design and planning. Control of PDEs: fluid flow and vibration control, actuator design, computational statistics.