Abstract: This lecture is concerned with ordinary differential equations (ODEs) exhibiting two time scales, which are called slow-fast systems, or singularly perturbed ODEs. In the first part we will give an intuition of what a singular perturbation problem is, how they appear in the context of ODEs, and some basics about the geometric theory available for their analysis. In the second part we will provide a few examples where the theory has been used to explain surprising phenomena in relatively simple systems. One interesting application we shall cover is related to consensus dynamics.
Title: Wave equations with fractional loss operators
Abstract: In the fields such as medical ultrasound imaging or elastography, waves travel through media which causes a frequency-dependent reduction of amplitude. It has become evident in recent years that these attenuation laws are more complicated than initially thought and that wave equations with fractional loss operators are needed to model such behavior. In this lecture, we will discuss energy methods in the well-posedness analysis of such equations. In the first part, we will focus on linear equations with time-fractional damping and contrast the Faedo-Galerkin approaches in their well-posedness analysis with that of their integer-order counterparts. The second part will focus on the challenges of extending these results to nonlinear wave phenomena, which arise when considering, e.g., sound waves at high intensities
Title: Data science in public health
Abstract: Data science, machine learning, artificial intelligence. What is all the buzz about and what position do they have at the National Institute for Public Health and the Environment (RIVM)? In this talk I will share some day to day experiences at the RIVM, some interesting data science use cases, and the knowledge and experience a PhD in nonlinear dynamical systems has brought me in this career path.