ERC Starting Grant (ERC-2016-STG): GeoMeG - Geometry of Metric groups
What are the best trajectories for parking a lorry with multiple trailers? How fast can a lattice grow? What are the minimal perimeter sets in geometric models beyond Euclidean space? These are some of the questions studied in Enrico Le Donne's European project. Since March 2019 Enrico Le Donne has been in post as Full Professor at the Department of Mathematics, thanks to the University incentive of the direct call for ERC grant winners. His project GeoMeG - Geometry of Metric groups was awarded €1.25m by the European Research Council, the majority of which were transferred to the University of Pisa from the Jyväskylä University of Finland. The project is being developed in parallel with an equally prestigious "research fellowship" awarded to Prof. Le Donne by the Academy of Finland (AKA).Both projects study new mathematical formalizations created by the interaction between algebraic structures and non-Euclidean geometries, giving rise to geometric models that can be applied in diverse fields, for example in the driving of computerized vehicles (multi-trail trucks), in the most modern computer-managed car parks (cooperative self-driving cars), in satellite technology and in the study of visual images, with recent developments in research on patients with diabetes.
"My team and I study geometric structures from an abstract point of view," says Le Donne. "However, they have potential applications in control theory and neuromathematics," he adds. One of Le Donne's most significant achievements was obtained in collaboration with one of his students, Eero Hakavuori. The result implies that when driving a truck in an optimal way, you never need to turn the steering wheel quickly. Now Le Donne and his colleagues want to formally demonstrate this. In other words, they want to show that the best way to drive a truck is to drive "smoothly". Mathematics is divided into several areas, such as algebra, geometry and analysis. Le Donne's project extends to all of these areas and its expected results will provide links between them.
Thanks also to his brilliant early international career, Le Donne has developed a dense network of high-level collaborations with researchers from America, Australia, Asia and various European locations. Le Donne graduated from the Scuola Normale Superiore in Pisa and did his PhD at Yale University (Connecticut, USA). At Jyväskylä University, he obtained his permanent position only three years after graduation. Previously, he worked at ETH (Switzerland), Orsay (Paris) and MSRI (California). In 2015 he received the prestigious position of researcher at the Academy of Finland.
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