State of the Art

Brazilian Mathematics enjoys solid international prestige, that deserves it the membership of the Group III in the International Mathematical Union, together with Australia, Belgium, China, Hungary, Holland, India, Poland, and Spain, a very good global indicator of the level of its research and scientific activities. It is necessary, however, that the mathematical community address the demands for association with other areas of scientific knowledge, and with the productive sector, besides giving a vigorous contribution to the improvement of education, at all levels, to the diffusion of knowledge and to the search of young talents. With this in mind, the present project must mobilize and integrate the most competent groups of mathematicians, in order to attain, in the next 3 or 4 years, a new level of excellency, with a broader scope of research, while keeping its high standards, and the participation of a larger group of researchers, both at the national and the regional level. Accordingly, a substantial increase of relevant scientific results is expected, in the fundamental areas of Mathematics, as well as concerning its applications and computational modeling, and also in the education of young researchers, creation and consolidation of new groups, and significant contribution to the mathematical education, again at the national level.

The above diagram illustrates the connections between the various aspects of the proposal. A detailed presentation of the scientific and technological background of the proposal is given below, including some of the main results already obtained by the participating teams, together with their main objectives.

1. Mathematical Modeling of Biological Systems
2. Computer Graphics
3. Optimization and Electrical Energy
4. Differential Geometry
5. Algebra and Algebraic Geometry
6. Mathematical Economy and Finances
7. Control Theory
8. Partial Differential Equations
9. Operator Algebras and Harmonic Analysis
10. Combinatorics and Algorithms
11. Petrol
12. Weather Prediction and Climate
13. Dynamical Systems
14. Probability
15. Topology and Singularity Theory
16. Mathematical Teaching and Olympiads
17. Cooperation with Latin America