Partial differential equations

…Themes include variational models and partial differential equations, homogenization, inverse problems, image analysis, nonlinear elasticity, phase transitions and pattern formation. Research on soft, active, optical, topological and other functional materials is considered alongside electronic structure, quantum approaches, machine learning and data-driven methods.

…including numerical analysis and partial differential equations, with two courses per semester. Applications require a cover letter, CV, research and teaching statements, publication links, evidence of effective teaching and at least three references. Review begins on 1 November 2026 and continues until the position is filled; the advert requests reference letters by that date.

Optimal transport is a mathematical method to define a distance between probability distributions. This is particularly useful in various domains, including physics, biology, machine learning, and economics, among others. After introducing the Optimal Transport (OT) problem at finite temperature, we show how it can be formulated as a statistical physics problem. This approach allows us to derive very efficient algorithms to effectively compute the distance between two probability distributions. The a priori unrelated Schrödinger bridge (SB) problem is presented, and it is shown to be a dynamic

…tool for solving and exploring partial differential equations. Examples include airborne infection and flood-water movement. The conversation covers why the tool was built, how interactive simulations make models understandable to non-specialists, and how researchers can quickly investigate the behaviour of their equations.

Unsupervised segmentation of behavior and neural activity into simpler alternating states is providing unprecedented insights onto the neural underpinnings of decision-making. Recurrent Switching Linear Dynamical Systems (rSLDS) models use observations or continuous latent activity to guide the switching in states, providing significant advantages in capturing important temporally and spatially sequential dependencies. In trying to allow for unbounded complexity in the discrete states, most approaches have focused on Dirichlet Process (DP) mixture models. Such non-parametric Bayesian models re