Multiple Time Scale Dynamics: From Finite to Infinite - Christian Kuehn

Abstract:

Systems with multiple time scales appear in a wide variety of applications. Yet, their mathematical analysis is challenging already in the context of ordinary differential equations (ODEs), where about four decades were needed to develop a more comprehensive theory based upon invariant manifolds, geometric desingularization, asymptotic analysis, and many other techniques that span across the mathematical sciences. This framework has become known as geometric singular perturbation theory (GSPT). Yet, for stochastic and spatial systems there are many obstacles in generalizing existing ideas. In this talk, I will first provide an introduction to multiple time scale dynamics and then outline two recent advances of the field, where I have contributed: (1) early-warning signs for bifurcations of stochastic multiscale systems, and (2) new invariant manifold and blow-up methods for PDEs. These advances illustrate nicely the breadth of the field spanning virtually all mathematical disciplines.

Bio:

Christian Kuehn is a Lichtenberg Professor for Multiscale and Stochastic Dynamics at the Technical University of Munich. He received his PhD in Applied Mathematics from Cornell University in 2010. Subsequently, he worked at the Max Planck Institute for the Physics of Complex Systems in Dresden as a postdoctoral researcher in network dynamics. From 2011 to 2016 he was a postdoctoral fellow at the Vienna University of Technology in the Institute for Analysis and Scientific Computing and a Leibniz fellow at MFO in 2013. He joined TUM as an assistant professor in 2016. Author of two books and more than 100 publications, his research interests lie at the interface of differential equations, dynamical systems, and mathematical modelling. A key goal is to analyze multiscale problems and the effect of noise/uncertainty in various classes of ordinary, partial, and stochastic differential equations as well as in adaptive networks. On a technical level, his work aims to build bridges between different areas of the study of dynamical systems.

Refreshments | 15:30 | Common Room Ground Floor

Meeting with Students | 16:15 | "What is the difference between pure and applied mathematics?"