October 30, 2026, Webb Hall 1100

Uncertainty frequently arises in complex systems to resolve microscopic or external processes. Yet, the analysis of the resulting models is extremely difficult, even numerically, as one has to cover large sample spaces. This is usually impossible even with ideal computational resources, and the problem becomes prohibitive if we rely upon data-driven representations of dynamics or just have limited observable data available. In this talk, I shall illustrate how numerical continuation methods can be lifted to random and stochastic systems. Numerical continuation methods are one of the most common and dimension-friendly tools in the applied sciences to understand nonlinear dynamics so extending them has the potential to be very impactful in stochastic modelling. The key technical idea is to obtain deterministic governing equations for key stochastic observables and then exploit these directly inside predictor correct schemes to study dynamics such as invariant sets and bifurcations. The presentation is joint work with several colleagues over several years, which has culminated into a large numerical continuation framework for random and stochastic systems.

The research interests of Christian Kuehn 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 and polyadic networks. The phenomena of central interest are: patterns, bifurcations and scaling laws. On a technical level, Kuehn's work aims to build bridges between different areas of the study of dynamical systems.

After studying mathematics at Jacobs University Bremen (BSc 2005) and at the University of Cambridge (M.A.St. 2006), Kuehn 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 the field of network dynamics. From 2011 to 2016 he was an Austrian Academy postdoctoral fellow at Vienna University of Technology in the Institute for Analysis and Scientific Computing and a Leibniz fellow at MFO in 2013. He is Lichtenberg Professor for Multiscale and Stochastic Dynamics at TUM.