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?Prof. Florian Luca, a number theorist in Stellenbosch 中国体育彩票's (SU) Department of Mathematical Sciences, is one of three principal investigators who have been awarded a Synergy Grant to the value of �7.5 million (about R143,1 million) from the European Research Council (ERC).
The other two principal investigators are Prof. Valérie Berthé from the French Institut de recherche en informatique fondamentale at the Centre National de la Recherche Scientifique (CNRS) at the 中国体育彩票 Paris Cité, and Prof. Jo?l Ouaknine, Scientific Director at the Max Planck Institute for Software Systems (MPI-SWS) in Saarbrücken, Germany.
The ERC Synergy Grants foster collaboration between outstanding researchers, enabling them to combine their expertise, knowledge and resources to push the boundaries of scientific discovery. The funding is part of the European Union's Horizon Europe research and innovation programme. The competition for this year's funding round was intense, with only 57 (10.4%) proposals out of a total of 548 succeeding.
Over the next six years, this multidisciplinary team from the fields of number theory and theoretical computer science are taking a “high-risk, high gains" approach to tackle one of the key computational challenges represented by so-called “discrete dynamical systems" – that is, systems that change over time following specific rules.
According to a media release issued by the Max Planck Institute, creating algorithmic solutions to make these systems amenable to automated verification techniques remain a major challenge, especially in fields such as program analysis and computer-aided verification to artificial intelligence and theoretical biology.
“The paradigm of 'model checking' is a powerful method that allows us to automatically verify, with mathematical certainty, whether a system behaves as intended," explains Prof. Ouaknine. However, many discrete dynamical systems cannot currently be verified with the available model-checking approaches.
One of the leading objectives of this new research project, titled “Dynamical and Arithmetical Model Checking (DynAMiCs)" is to substantially broaden the classes of dynamical systems and properties that can be algorithmically handled via model checking. Specifically, it aims to tackle longstanding mathematical challenges, such as the Skolem Problem, that could lead to breakthroughs in understanding and verifying the behavior of other complex systems.
Prof. Luca says their successful proposal is based on a very firm research foundation: “My cooperation with Jo?l's team started in late 2019. At that time, I was a visitor at the Max Planck Institute for Mathematics in Bonn and he and his team came from Saarbrücken looking for mathematicians who would be interested in working on problems from the field of theoretical computer science."
Since Prof. Luca is already well-known as a “problem-solver" amongst peers and colleagues, the Saarbrücken team was advised to meet with him.
“Since that first meeting, I would spend a few months per year at the Max Planck Institute for Software Systems working with Jo?l and his group. By now we have published some 15 papers in which we made substantial progress on some hard problems. The idea of applying for an ERC grant came at a workshop in Barbados in May last year where Valérie from CNRS, Jo?l and I were all present and for the next five months we worked on the proposal," he explains.
It took 11 months and various steps, including an in-person interview at the ERC headquarters in Brussels on 10 September 2024, where they had to present their project and answer questions from a panel of 20 specialists.
Prof. Luca says most of the grant will be used to hire postdoctoral fellows and PhD students to help advance the project and contribute to training a new generation of researchers. The team is also planning two summer schools and several seminars and workshops.
While he will be working at the Max Planck Institute for six months of the year, his research group here at SU will work on the project full time. There will also be opportunities for exchange programmes between the institutions and many other collaborators involved.
For now, postgraduate students interested in joining this project should watch out for the first advertisements going out in December and January next year. The project starts officially in March 2025, and Prof. Luca will leave for his first stint of six months at the Max Planck Institute after the end of the first semester.
“Because of my unique position of being able to cooperate with both the National Research Foundation via SU and being a principal investigator of an ERC funded team, I hope to be able to bring some South African students and postdocs to either be part of the ERC team or to visit for various periods of time with the above (or some other similar) opportunity," he concludes.
Prof. Ingrid Rewitzky, SU's Head of the Department of Mathematical Sciences and the Faculty of Science Vice-Dean: Teaching and Learning, congratulated Prof. Luca on this excellent achievement: “We are excited about the opportunities for researchers, postgraduate students and postdoctoral fellows to collaborate with this inspiring DynAMiCs team. As a department, we look forward to hosting team members of the DynAMiCs project for research visits, collaboration and jointly hosting research workshops and seminars."
Image credit: Stefan Els
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