Geometry and Non-Linear Methods
The research theme is addressed by a project which articulates the graduate programs in Mathematics (grade 7), Teleinformatics Engineering and Economics (grade 5), whose driving force is the use of geometrical and analytical methods in the theory of information and signal processing, with applications in telecommunications engineering and finance. The GP in Mathematics is one of the pioneers, even in national scale, in terms of international collaborations formalized along the years, in several agreements and projects, for instance, Pronex, COFECUB, Science Without Borders, among others. The GP in Mathematics was promoted to grades 6 and 7 in consecutive assessments carried out by CAPES, whereas the GP in Teleinformatics Engineering, despite its recent creation, was promoted to the international excellence grade. Such changes of level are mostly due to the emphasis of the programs in international cooperation. Researchers from both GPs have taken part in joint research projects, funded by development agencies, some of them with a counterpart of foreign institutions. Recently, the research interests, originally focused on geometrical, dynamic or analytical aspects of signal processing and optimization in the presence of curvature, derived to possibilities of application to finance of the machine learning methods adapted to non-linear or singular settings. With these outcomes, the projects started to involve researchers from the GP in Economics, a nationally consolidated program and with an intense history of collaborations for the management of public finances in the state of Ceará. The project aims at integrating these internal collaborations and the foreign cooperation network maintained by the most internationally consolidated programs, involving, in the present proposal, prestigious American and French universities. The theme involves applications of the language, dynamics and analysis of geometry, especially in singular or stratified spaces, to research topics in areas such as complex systems, for example, the relationship between stochastic processes and phase transitions, and information geometry, in which the geometric nature of statistical manifolds in applications to signal processing is explored, especially in the form of sets of big data about financial assets.
