Dr. Andrew Krause, Durham University, UK
Abstract: Natural patterns, such as those created during embryological development, can arise from enormously complex processes occurring across vast scales of space and time. A key scientific challenge is to conceptually map out these processes in terms of distinct mechanisms, and their interplay. Dynamical systems theory provides several tools for developing hypotheses regarding such processes, and for understanding the limitations of potential mechanisms.
We will discuss the uses and limitations of linear and nonlinear analyses of reaction-transport models in the context of understanding problems of multiscale periodic patterning. A focus will be on understanding robustness and the ability for 'generic' models to exhibit different patterning behaviours, without having to quantify molecular details of a particular system. We will aim to demonstrate how these kinds of models and ideas can help generalize insights from specific systems and numerical simulations, while also discussing fundamental limitations to this kind of modelling. VisualPDE.com will be introduced as a tool to rapidly prototype simple models, as well as to teach and communicate aspects of PDEs more generally. We will end with a range of open problems, both technical and conceptual.
Bio: I am an Assistant Professor in Applied Mathematics at the Department of Mathematical Sciences at Durham University. I am primarily involved in teaching and research within mathematical biology and nonlinear dynamical systems, but I am also interested in broader scientific and philosophical themes. I am chronically-ill and legally blind (very nearsighted).
I grew up in New Mexico, USA, where I earned undergraduate degrees in Mathematics and Computer Science at the New Mexico Institute of Mining and Technology and a Masters degree, in Mathematical Analysis. I then obtained a DPhil (PhD) in Mathematics within the Oxford Centre for Industrial and Applied Mathematics, and continued as a postdoc in the Wolfson Centre for Mathematical Biology before becoming a Departmental Lecturer in Applied Mathematics jointly between these two groups. I then joined Durham in 2021.
Meeting ID: 998 2458 4542
Passcode: 475065