M4 Science and Knowledge
The generation of mathematical knowledge is essential for the development of science. Advances motivated by curiosity are the seed of future applications to other sciences, which may end up shaping the progress of our society and the development of innovative technologies. The research and transfer area M4 Science and Knowledge encompasses the development of new ideas, tools and results aimed at going beyond the state of the art of mathematical knowledge, especially in aspects of great interest within Mathematics or in relation to other sciences.
We collect in three PIs different lines of research with this general objective.
PI Dynamics and complex phenomena: As the nature of complex phenomena is diverse, the understanding and explanation of different processes leads to various mathematical objects: discrete dynamical systems, ordinary differential, difference or stochastic equations, special functions, orthogonal polynomials, foliations, geometric evolution equations, networks, game theory and operations research models, regression models, etc. The focus is the design of well-defined and robust mathematical models that capture the essence of the phenomena of interest.
PI Natural Structures: This PI addresses the development of fundamental ideas and results naturally motivated by the mathematical study of space and form, mathematical symbols and their rules, and the relationship between them.
PI Mathematical data analysis: The widespread availability of computing power that allows in silico simulations using mathematical models, as well as the explosion in the amount of data that is being collected or generated (available to a large extent through the Internet), is often such that it can only be evaluated through mathematical and statistical techniques, which will be essential, not only for reproducing accurate models, but also for developing data-driven models of highly complex phenomena, as well as for the use of data assimilation techniques applied to a growing number of challenges.