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.

Hessian-dependent functionals play a pivotal role in a wide latitude of problems in mathematics. Arising in the context of differential geometry and probability theory, this class of problems find applications in the mechanics of deformable media (mostly in elasticity theory) and the modelling of slow viscous fluids. We study such functionals from three distinct perspectives.

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.

Panel Discussion for the Masterclass on Semiconductor Photonics.

Integrated Si photonics has sparked a significant ramp-up of investment in both academia and industry as a scalable, power-efficient, and eco-friendly solution. At the heart of this platform is the light source, which has been the focus of research extensively. (...). Click on the talk for more information.

This talk summarizes recent research results in the field of universal light encoders. (...). Click on the talk for more information.

This talk explains the cutting-edge technology of micro-LEDs. (...). Click on the talk for more information.

This talk focus on the recent progress of visible diode laser-based lighting technology and high-speed transmitters and receivers for Gbit/s visible light communication (LiFi) and underwater wireless optical communication. (...). Click on the talk for more information.

This talk presents selected topics in science and engineering from an applied-mathematics point of view. (...). Click on the talk for more information.

This talk describes the rich connections between the physical notion of diffusion and mathematical regularity estimates of solutions of the driving PDEs. (...). Click on the talk for more information.

This talk explores connections between some Partial Differential Equations, Fourier Analysis, and real-life problems. (...). Click on the talk for more information.

This talk presents certain topics of interest in Prof. Tzavaras's group concerning the study of fast flows in fluid mechanics and the theory of Hyperbolic Conservation laws and Hyperbolic-Parabolic Systems. (...). Click on the talk for more information.

This talk derives a quantitative modulus of continuity, up to the parabolic boundary, for solutions of the Cauchy–Dirichlet problem associated with a phase transition modeled upon the p-degenerate two-phase Stefan problem. (...). Click on the talk for more information.

This talk explores the connections between optimal control problems and machine learning. (...). Click on the talk for more information.

Several physical systems are described by evolutionary partial differential equations describing rarefied gasses, (...). Click on the talk for more information.

This seminar focuses on machine learning (the computers’ ability to learn based on training from large data sets) and computational science (...). Click on the talk for more information.

This talk will review the recent shift in the construction and modern analysis of a large class of spatially (...). Click on the talk for more information.

Since the celebrated paper by Lax and Wendroff, it is known what kind of structure should have a numerical scheme to (...). Click on the talk for more information.