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Applied Mathematics
From its inception, one of the aims set out for the present Division of Mathematical Sciences was that it ought to transcend the traditional division of mathematics into algebra, geometry and analysis and that, on the contrary, it should incorporate those three areas into a larger field of mathematical interest, which can be called the mathematical sciences. The way this endeavour was conceived at the outset, was to "treat the study of mathematical models for various phenomena as well as the mathematical construction of such models as a whole", the mathematical investigation of which would then be the focus of future research.
As this goal can surely not be met by applying only established mathematics, the development of new mathematical theories adapted to such problems becomes a major goal in itself.
The members of the applied mathematics section strive to embody this idea, but as its multifaceted nature renders any attempt at general theory futile, their research activities can best be grouped into four themes:
- Modelling and analysis of natural and sociological phenomena; important research themes include: the mathematics of nonlinear phenomena, nonlinear dynamics, nonlinear wave theory, computational mechanics, mathematical biology and demography, and mathematics of fluid phenomena.
- The study of the algebraic, geometric and analytic structures inherent in mathematical phenomena. In particular: numerical analysis, field theory, string theory, integrable systems, statistical mechanics, soliton theory, the study of Painlevé-type equations and of the Navier-Stokes equation.
- Probability theory and mathematical statistics. In particular, stochastic analysis, semimartingale theory, Malliavin calculus, Lévy process, limit theorems, asymptotic expansion, theoretical statistics, asymptotic decision theory, statistics for stochastic processes, statistical learning theory, quantitative finance, stochastic numerical analysis, and biostatistics.
- Computer Science, in particular the mathematical foundations of programming languages and proof theory.
