FCT

R&D Institutions

Resultado da avaliação 2007 na área de Matemática

Unidade de I&D

Centro de Análise Matemática, Geometria e Sistemas Dinâmicos [MATH-LVT-Lisboa-89] visitada em 21/02/2008

Classificação: Excellent

Comentários do painel de avaliação
Sobre a unidade
The Center continues to be an outstanding research unit in Portugal.

The areas of emphasis are nonlinear analysis and differential equations, dynamical systems, geometry and topology, and mathematical physics. The Center exhibits impressive breadth and strength in all these topics with activities and publications in dynamical systems and ergodic theory; equivariant dynamics; ordinary, partial and functional differential equations; calculus of variations and optimization; geometric, topological and algebraic methods in nonlinear analysis; control theory; mechanics of continuous media; algebraic, differential, symplectic and combinatorial geometry; general relativity; Yang-Mills and Chern-Simons theory; and string theory. These are all topics of current and general interest to the international mathematical and scientific community.

The breadth is possible because this is a one of the largest centers, relatively young, and most of the members have been trained at top universities around the world. Also, it runs a large postdoctoral program where a large majority of the postdocs have been recruited from abroad with degrees from premier departments including Cambridge, Columbia, Illinois, and Warwick. Most of the members are publishing regularly in the best international journals. The work is kept topical by a constant stream of high profile international visitors; more than a half dozen regular seminars on distinct topics; and conferences and short courses of varying size and emphasis.

Many of the mathematical topics emphasized by the Center have immediate applications. In line with previous recommendations the Center show greater interest in realistic applications, the Center has signed partnership protocols with the Institute for Systems and Robotics and the Institute of Telecommunications. In addition is has established an innovative seminar series with the Institute for Systems and Robotics designed to foster interactions.

The Center is actively involved in mathematical education and outreach at all levels. It has established a well structured graduate program along the style of an American graduate program with a well defined first year of graduate level mathematics courses. Furthermore, they appear to have a steady stream of graduate students producing high quality PhD theses. The proposed joint UNL, IST and UL graduate program along with exchange program with the University of Texas- Austin and Carnegie-Mellon University will add critical mass to this effort. Members of the Center have been active in the creation, planning, management, and teaching of the Undergraduate Program in Applied Mathematics and Computation. They have started to develop a network of high school Mathematics teachers to foster discussion on methods, materials and other pedagogical aspects of the teaching of Mathematics. This has been followed up with formal partnership protocols with 44 schools which together enroll more than 28,000 students.

The members of the Center are justifiably proud of their accomplishments. They have succeeded by adopting and persevering with a particular model that is based on building and maintaining a critical mass at the IST. This includes recruiting strong people in targeted areas of research, maintaining a harmonious group, providing an excellent intellectual environment, and building adequate working conditions. At the moment, however, the members appear to be worried that they have reached a juncture - they must either move to a higher level or face stagnation and a decrease in their quality. Furthermore, they express frustration at structural barriers associate with their status as a research unit that are preventing them from improving.

The panel is sympathetic to these concerns and is strongly supportive of their efforts to attain the stature of an associated lab. In line with the previous panel's report we believe that this "could become a reference and a mobilizing example in Portugal." However, as the previous report suggested this also calls for an expansion of the vision and activities of the Center. There continues to be limited interest in the use of "computational tools not only as a source of new problems, but also as a tool to suggest/validate theoretical findings." Furthermore, given the proximity of dynamical systems and nonlinear analysis to all of science, engineering, social science, and medicine greater breadth of applications can be expected and encouraged. In addition, there are other research groups in the country and Lisbon that could be natural allies in the Center's goal of becoming an associated lab. Finally, given the current level of research and activities at the Center, improvement can only occur by the Center expanding its direct influence beyond the borders of Portugal and taking the lead in European based research initiatives.
Sobre os grupos de investigação
Centro de Análise Matemática, Geometria e Sistemas Dinâmicos [RG-MATH-LVT-Lisboa-89-495]