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Newton's legacy has inspired generations of mathematicians who have dedicated their lives to the study of motion in all its shapes and forms. His accomplishments have provided the cornerstone to advance the study of movement in probability theory, stochastic calculus, classical mechanics and partial differential equations, to name but a few. As movement processes are ubiquitous, and occur in response to signals acting across multiple scales, these areas of mathematics have advanced due to an influx of problems from across the entire scientific spectrum creating a set of concepts, tools and techniques that may be collectively termed the mathematics of movement. While the external influx of problems has been instrumental in realising a high level of mathematical sophistication, it has created cultural and technical barriers between movement modellers working in different disciplines.
The goal of the programme is to transcend these barriers by focusing our activities on movement phenomena in animal ecology and cell biology. Over the past decades, these two disciplines, have witnessed tremendous advances in tracking technologies and imaging tools bringing unprecedented resolution and quality to movement data. The quantitative techniques to analyse and interpret such data have also leapt forward, bringing an ever increasing level of mathematical and computational sophistication in movement models. We aim to catalyse the conceptual and technical integration of these advances, bringing together empiricists and theoreticians, to facilitate the emergence of radically new ways of mathematical thinking to address the complexities of movement, from individual to population level descriptions, from stochastic to deterministic models, from transient dynamics to long-term dependencies, and from spatio-temporal techniques to network approaches.
We have identified three principal areas that are ripe for a cross-disciplinary approach. These areas, associated with the three workshops that will be run during the programme, are (i) Collective behaviour (ii) Measures and representations of interaction, and (iii) Non-Markov movement processes. At the start of the programme there will be a summer school where state-of-the-art models and techniques on these topics will be explored.
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