Rate My Professor Andrew Krause

Dr. Andrew Krause is an Associate Professor in Applied Mathematics in the Department of Mathematical Sciences at Durham University. His research specializes in mathematical biology and nonlinear dynamical systems, focusing on pattern formation, Turing instabilities, reaction-diffusion systems, and partial differential equations. Krause investigates how spatial heterogeneity localizes patterns, the limitations of Turing instabilities for ensuring pattern emergence, and the dynamics of cross-diffusion models relevant to chemotaxis and ecological interactions. He has authored numerous publications in prestigious journals, including 'Turing Instabilities are Not Enough to Ensure Pattern Formation' (Bulletin of Mathematical Biology, 2024), 'Pattern Localisation in the Swift-Hohenberg Equation via Slowly Varying Spatial Heterogeneity' (SIAM Journal on Applied Dynamical Systems, 2025), 'VisualPDE: Rapid Interactive Simulations of Partial Differential Equations' (Bulletin of Mathematical Biology, 2023), 'Spatial heterogeneity localizes Turing patterns in reaction-cross-diffusion systems' (Discrete & Continuous Dynamical Systems - B, 2023), and 'Modern perspectives on near-equilibrium analysis of Turing systems' (Philosophical Transactions of the Royal Society A, 2021). These works explore bespoke Turing systems, wave instabilities, and the role of transport in biological patterning, contributing to over 1,350 citations on Google Scholar.

Prior to his appointment at Durham University in 2021, Krause was a Postdoctoral Research Associate at the University of Oxford Mathematical Institute, where he earned teaching accreditation. He served as Lead Guest Editor for the Philosophical Transactions of the Royal Society A theme issue 'Recent progress and open frontiers in Turing’s theory of morphogenesis' (2021). Krause co-developed VisualPDE.com, an open-source platform for interactive PDE simulations used in research and education. He contributes to pedagogy through interactive visualisations, alternative assessments, and inclusive teaching, and is a member of Durham's First-Generation Scholars network. His interdisciplinary collaborations bridge mathematics with biophysical sciences, influencing studies on fingerprint formation, bat teeth evolution, and cancer immunotherapy resilience via pattern mechanisms.