The Laboratoire d'Excellence Bézout is structured by four main scientific areas, at the interface between mathematics and computer science:
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Discrete mathematics and Algorithms: A major technological challenge is to find efficient automatic ways of sorting very large data or data sets of various kind such as textual, linguistic or biological data, or mutimedia. We plan to answer it using formals models and syntactic methods (automata, graphs, ergodicity, formal grammars, combinatorial structures, …) and also analysis tools (multifractals) to structure, classify and index these data. We will design probabilistic or approximate algorithms and also develop statistical methods (kernel methods, bootstrap).
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High dimensional phenomena: High dimensional phenomena are ubiquitous in modern applications, such as in telecommunications, genomics, and imaging. The mathematical and algorithmic analyses underlying these models involve deep tools from asymptotic geometric analysis, random matrices, and combinatorics. In particular, random matrix theory (RMT) became a key tool in these questions and will play a central role, since it is at the heart of mathematical and computational challenges.
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Stochastic and deterministic models: Mathematical finance and computational models in physics and biology lead to hot scientific problems which combine stochastic and deterministic modeling, and require the development of suitable analysis concepts and tools. This constitutes an emerging area of research where significant advances in several fields of application can be expected. The main tools are stochastic analysis and Markovian dynamics.
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Images and geometry: Computer imagery, such as 3D photography and medical image analysis motivates many examples of open mathematical problems. For example, a fundamental subject is the study of relationship between the approximate discrete model and geometric invariants computed on smooth shapes (such as conformal parametrizations, mean curvature, Gauss curvature, or umbilical points).
Several world famous scientists are scientific animators of the Bézout Labex:
- Jean Berstel is Docteur Honoris Causa of Turku University.
- Philippe Biane received the Rollo-Davidson award (London Math. Soc. 1995) and the Lecomte award (French Academy of Sciences, 1998).
- Eric Cances received the Blaise Pascal award (French Academy of Sciences and SMAI, 2009).
- Raphaël Danchin received the Audin Prize in 2009.
- Bernard Host is senior member of the Institut Universitaire de France. He received in 2005 the "Charles-Louis de Saulses de Freycinet" award of the French Academy of Sciences.
- Stéphane Jaffard is former junior member of the Institut Universitaire de France.
- Claude Le Bris has been awarded the Aisenstadt Chair for 2009-2010 from the University of Montréal and has delivered a series of lectures at this occasion.
- Tony Lelièvre shared the Alcan Prize 2010 (French Academy of Sciences).
- Etienne Sandier is junior member of the Institut Universitaire de France.
- Hugues Talbot received the “Society of Australian Engineers” award in 2005 and the DuPont award in 2006.
- Jean-Yves Thibon is senior member of the Institut Universitaire de France.
