The ChaParDyn project is focussing on so-called parabolic dynamical systems: mathematical models for the many phenomena which display a "slow" form of chaotic evolution. Examples of parabolic systems span from famous physics models, like the Novikov model describing electrons in metals, to fundamental mathematical objects, such as flows on surfaces.

Prof. Ulcigrai, who leads the project, explains, “When it comes to parabolic dynamical systems, the problem is that only few examples are understood well and have been studied in depth. Each example tends to display different chaotic features, so it's hard to identify common phenomena and mechanisms for chaos.”

Many of the parabolic systems we know best have a form of ‘homogeneity’, and in some sense have a lot of internal structure. One of the project components is to study ‘perturbations’ of this system, where this homogeneity and structure breaks down. For these ‘inhomogeneous’ systems, one cannot use algebraic tools, but some geometric features still persist and can be exploited.

While fundamental research, such as that carried out by Prof. Ulcigrai, is not driven by potential applications of results, virtually all of the systems that impact our everyday lives are chaotic, so ‘understanding chaos’ mathematically is essential. The project’s research highlights the central role played by geometric phenomena in explaining the features of ‘slow chaos’. The project also demonstrated that when homogeneity is broken, typical features do indeed seem to appear, which gives hope for a unifying description.

Corinna Ulcigrai studied at the Scuola Normale in Pisa (Italy) and received her PhD from Princeton University under Y. Sinai in 2007. She became Full Professor at the University of Bristol in 2015 and at the University of Zurich in 2018. Her awards include a European Mathematical Society Prize (2012), a Whitehead Prize (2013) and a Wolfson Research Merit award (2017).