As Einstein Postdoctoral Fellow at Freie Universität Berlin, mathematician Tobias Hurth focusses on random processes. Such processes and their parameter-dependent changes are omnipresent in science and technology, but the mathematical theory concerning bifurcations in such systems is still in its infancy. Together with the head of the Junior Research Group at the MATH+ Excellence Cluster, Maximilian Engel, Hurth will look to apply key cornerstones of ergodic theory to localized random processes as well as analytically and numerically developing the stochastic bifurcation theory. His analysis will focus primarily on Lyapunov exponents, which are key to forming an appropriate idea of entropy and equilibrium states. The theoretical insights obtained here could also help gain a better understanding of chemical reaction networks. The team of researchers led by Maximilian Engel will attempt to establish stochastic bifurcations so that this analysis can be applied to biological models of gene expression, cell growth, and random dynamics in deep neuronal networks.
