Parabolic partial differential equations (PDEs) play a pivotal role in modelling processes that involve diffusion and thermal dynamics. Over recent decades, the study of their controllability – the ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

Partial Differential Equations (PDEs) are mathematical equations that involve unknown multivariate functions and their partial derivatives. They are the cornerstone of modelling a vast array of ...

Last year, MIT developed an AI/ML algorithm capable of learning and adapting to new information while on the job, not just during its initial training phase. These “liquid” neural networks (in the ...

In this topic, our goal is to utilise and further develop the theory of non-linear PDEs to understand singular phenomena arising in geometry and in the description of the physical world. Particular ...

An advanced course in the analytical and numerical study of ordinary and partial differential equations, building on techniques developed in Differential Equations I. Ordinary differential equations: ...

Partial differential equations (PDEs) lie at the heart of many different fields of Mathematics and Physics: Complex Analysis, Minimal Surfaces, Kähler and Einstein Geometry, Geometric Flows, ...