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Ch. Kuehn:
"A Mathematical Framework for Critical Transitions";
Talk: Max Planck Institut DS Advances Seminar, Göttingen (invited); 2013-07-04.

In this talk he will outline a basic mathematical theory for critical transitions in fast-slow stochastic systems with loss of normal hyperbolicity. It is shown that this framework encompasses various effects and requirements found in the last decade in widely disparate application areas. In particular, we will state and discuss a theorem on scaling laws of covariance matrices for all bifurcations up to co-dimension two. An example from biomechanics and control will be given. Furthermore, I will outline several new research directions in multi-time-scale stochastic systems near instability: stochastic PDEs, self-organized criticality and large-scale biomedical data analysis.