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The School of Mathematics and Statistics is delighted to announce that Â鶹Éçmadou Scientia Professor of Mathematics, Gary Froyland, is the recipient of the , presented by the Society for Industrial and Applied Mathematics (SIAM).

Professor Froyland received the award for his work on , published inÌý which significantly advances the theory of complex fluid flow with application to climate science. Professor Froyland’s collaborators include Dimitrios Giannakis (Dartmouth College),ÌýBenjamin R Lintner (Rutgers University),ÌýMaxwell Pike (NOAA), andÌýJoanna Slawinska (Dartmouth College).Ìý

The JD Crawford Prize is awarded every two years for recent outstanding work on a topic in nonlinear science, as evidenced by a publication in English in a peer-reviewed journal within the four calendar years preceding the award year. The term ‘nonlinear science’ specifically includes dynamical systems theory and its applications as well as experiments, computations, and simulations.

Professor Froyland specialises in dynamical systems, machine learning, and optimisation. His research spans pure and applied mathematics, with applications in industry and other scientific disciplines. He currently leads the Australian Research Council Laureate Centre for Dynamical Systems and Data at Â鶹Éçmadou Sydney.

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Why are you excited to receive the award?

Froyland:ÌýIt's gratifying to have the work I've done with my colleagues recognised in this way, and in my view, the award belongs equally to them. There is so much exciting research at the moment in dynamical systems. The field has a very healthy future and a lot to contribute to science and society.

What does your work mean to the public?

Froyland:ÌýI'm interested in several different aspects of dynamics. Nonstationarity, or time-dependence of the governing laws of processes, makes these processes more difficult to analyse by standard means, and some of my work addresses this. Another aspect is extracting information on differing temporal and spatial scales, particularly those scales that are longer or larger and reflect what humans observe in the natural world. Statistical properties of processes are also important, for example, the behaviour of fluctuations that diverge from the average and the likelihood of large excursions that lead to extreme events. In addition to the theory underlying these aspects, there are important computation issues related to working directly with data. In fact, nowadays, physics-based models are, to some extent, being replaced by data, and I am interested in developing reliable and efficient algorithms for dynamic data.

Could you tell us about the research that won you the award?

Froyland:ÌýThere were two main pieces of research. The first concerned a transfer operator approach for extracting long-lived cycles from time series, where the elements of the time series could be high-dimensional, for example a temporal sequence of images. This was joint work with Dimitris Giannakis, Benjamin R Lintner, Max Pike, and Joanna Slawinska. We showed that the arguments of the leading complex eigenvalues of the transfer operator provide the frequencies of nonlinear cycles embedded in the system. As an application of this research, we extracted a canonical representation of a strong El-Nino Southern Oscillation cycle based on spatial fields of sea-surface temperature.

The second piece of research concerned an extension of the dynamic Laplace operator to time-extended domains. The dominant eigenfunctions of the dynamic Laplacian encode coherent regions in time-dependent dynamical systems. In many real-world settings, coherent sets are continually forming and dissipating, and by constructing an inflated dynamic Laplacian on a spatiotemporal domain, we can capture this emergence and disappearance across time in a single eigencomputation. This was joint work with Peter Koltai (from the University of Bayreuth).