Deadline: 27 apr 2025

We are currently advertising two PhD positions at TU Delft. Each position emphasizes a different mathematical direction:

-Position 1: Finite-Dimensional Curved Context

This project will focus on the theoretical development of the Hamilton–Jacobi equation in curved spaces, drawing upon techniques from differential geometry. The candidate will explore the role of curvature in dynamic optimization problems and analyze how stochastic control theory extends to non-Euclidean settings. Methods from (sub)-Riemannian geometry, geometric analysis, and PDE theory will be essential.

-Position 2: Infinite-Dimensional Context in Optimal Transport

This project will extend the theory to infinite-dimensional spaces within the framework of optimal transport, the theory of how to best move “mass”. The candidate will explore how recent developments in this field can be applied to the study of Hamilton–Jacobi equations. This direction is highly relevant for applications in statistical physics, stochastic processes, and large-scale systems where transport and diffusion play a key role.

Both PhD candidates will be embedded in the Applied Probability group within the Department of Applied Mathematics, which has a strong research focus on controlled stochastic processes in contexts arising from statistical physics, finance, and beyond. The group also maintains close ties with the Analysis group, which specializes in the mathematical theory of partial differential equations, providing a rich and collaborative research environment.

• Link to the call