We will discuss the solution of eigenvalue problems associated with partial differential equations (PDE)s that can be written in the generalised form Ax = λMx, where the matrices A and/or M may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilised formulations are used for the numerical approximation of PDEs. With the help of classical numerical examples we will show that the presence of one (or both) parameters can produce unexpected results.

We present a theoretical analysis of the Weak Adversarial Networks (WAN) method, recently proposed in [1, 2], as a method for approximating the solution of partial differential equations in high dimensions and tested in the framework of inverse problems. In a very general abstract framework.

Analogies between financial markets and critical phenomena have long been observed empirically. So far, no convincing theory has emerged that can explain these empirical observations. Here, we take a step towards such a theory by modeling financial markets as a lattice gas.

Wave propagation and scattering problems are of huge importance in many applications in science and engineering - e.g., in seismic and medical imaging and more generally in acoustics and electromagnetics.

In this short course, we will introduce some elements in deriving the hp a posteriori error estimate for a high-order unfitted finite element method for elliptic interface problems. The key ingredient is an hp domain inverse estimate, which allows us to prove a sharp lower bound of the hp a posteriori error estimator.

This seminar will review the development of electromagnetic surfaces, as well as state-of-the-art concepts and designs. Detailed presentations will be provided on their unique electromagnetic features. Furthermore, a wealth of practical examples will be presented to illustrate promising applications of the surface electromagnetics in microwaves and optics.

The “KAUST Research Conference on New Trends in Biosensors and Bioelectronics” aims to give an overview of the most recent efforts in bioelectronics that tackle the “interface” problem and overcome the limits of the current technologies by generating new materials/architectures/device components. With its truly interdisciplinary nature, this conference will bring scientists from different disciplines together.