R&D Institutions

Resultado da avaliação 2007 na área de Matemática

Unidade de I&D

Centro de Matemática e Aplicações Fundamentais [MATH-LVT-Lisboa-209] visitada em 19/02/2008

Classificação: Excellent

Comentários do painel de avaliação
Sobre a unidade
CMAF was one of the first Portuguese research centres in the area of mathematics. For many decades it held its prestige and recognition as a national standard and played a pivotal role in the development of mathematics research in the country. With the creation of new centres, some reaching international levels of excellence in Lisbon, Porto and Coimbra; CMAF has had to re-assess its mission, to re-direct and re-align its efforts. CMAF has vigorously initiated its response to the concerns expressed by the panel of the previous evaluation, by discontinuing certain lines of research and adding new, contemporary research groups such as the one in Mathematical Biology.

The strengths of CMAF are in the areas of Logic, Differential Equations and Mathematical Biology.

The outreach activities of the unit are extensive, ranging from the involvement of unit's members in the direction of the Science Museum of the University of Lisbon to the creation of digitalized teaching and learning tools for high school students.

The ranking of the Unit reflects its reformulation, however the Panel urges the unit to continue its restructuring, stimulating and encouraging its members to be active in the pursue of external funding, of seeking partnerships in European projects and networks, and in improving the impact that mathematics developed in the unit has outside its own boundaries.
Sobre os grupos de investigação
Differential and Functional Equations [RG-MATH-LVT-Lisboa-209-1167]
This is an active group working on very contemporary problems, ranging from functional differential equations with delays, reaction-diffusion equations, elliptic equations and systems, and dynamical systems, to the study of Hamiltonian systems motivated by issues in epidemiology systems. In view of this motivation, the team is urged to strengthen contact with the group in Mathematical Biology.

The panel notes the similarities in interests between this group and the research unit CAMGSD at the IST.

The group has very good international visibility, a very strong publication record in top journals, such as Trans. AMS, Proc. AMS, Calc Var PDEs, J. Differential Equations, SIAM J. Math. Anal.

The training and supervision record of young researchers is solid.
Hyperbolic Systems and Singularities in PDEs [RG-MATH-LVT-Lisboa-209-1163]
This group has mainly two directions of research: hyperbolic conservation laws, Burgers-type equation, Schrodinger-type equations or systems, shallow-water models; the local study of systems of over determined linear partial differential equations near a singular point of its characteristic variety. The latter involves computing fundamental groups of the complement of links and their representations. It relies on the use of D-modules.

This work is technically extremely deep, but it is poorly cited. The group is encouraged to try to increase the impact of their results, possibly by increasing their participation in international conferences and by hosting leading international experts.

This group is well positioned to train young researchers, and it is urged to seek appropriate FCT funding through individual grants.
Logic [RG-MATH-LVT-Lisboa-209-1162]
This group works in several areas of modern mathematical logic, principally proof theory, model theory, complexity theory and the theory of computation. Some of their research involves applications of logic to problems in algebra and analysis, which is an important recent trend in logic.

This group has excellent international visibility, and although the trainees these researchers have had are of very high quality, the number of young researchers supervised is lower than what would be expected.

Given the number of researchers, the size of the research output is very high. This group publishes in leading algebra and logic journals. There are strong links with the Philosophy department, including co-supervision of MSc theses, and these lead to publications in philosophy journals.

The Unit has secured external (to FCT pluriannual) funding and it is urged to interact and partner with European networks. They should try to become a full node in the European model theory network (MODNET). They should try to foster links with the Logic and Computation group at the Technical University.
Mathematical and numerical methods in Mechanics [RG-MATH-LVT-Lisboa-209-1166]
The work of this group is mostly on calculus of variations and PDEs. There seems to be relatively little activity directed at numerical methods. A somewhat disconnected area is on the geometry of Kahler manifolds and submanifolds and harmonic maps. Future work on nonconvex variational problems, transport, superconductivity equations, etc, albeit interesting seems to be mostly in the nature of continuing past research projects, with little evidence that new directions are going to be followed.

The productivity level is good and the unit publishes in some leading journals.

Training is the weak point of the group. It's members have supervised several MSc but PhD training has been slow. Currently there are PhD students being co-supervised with researchers abroad (Pablo Pedregal, Spain).

The group has many collaborations with foreign researchers in good institutions mostly in Europe and Russia and the USA. The group is active in the organization of conferences, and in seeking external (to FCT pluriannual) funding. The group seems to unaware of the major structural, shape and material optimization initiatives, most importantly the major EU sponsored PLATO-N project, within the 6th Framework Programme (Aeronautics). See: http://www.plato-n.org/. Clearly the group would benefit from direct research collaboration with the PLATO-N project team.

The panel has been informed of the effort to create a geometry group. The panel is supportive of this activity and encourages its gradual evolution towards contemporary questions, for example, on the algebraic side, the rigidity problems in representation theory or, on the analytic side, the study of singularities of some harmonic maps. In addition, the Panel recommends that, rather than creating a new, separate group, this small cluster of researchers develop collaboration with the geometry group in the Instituto Superior Técnico and participate actively in the Lisbon geometry seminar.
Mathematical Biology [RG-MATH-LVT-Oeiras-209-1168]
The excellence of this group has been recognized with the award of a Marie Curie Excellence team grant. The research is focused on dynamical systems and stochastic dynamics to study epidemiology (malaria, pertussis, tuberculosis, etc.). Future work will be on applications of mathematics (dynamical systems, probability and statistics) to epidemiology, and brain sciences, threshold behaviour in epidemiology, neuroscience and environmental science.

The group has excellent visibility, excellent networking and participation in EC working groups, it has been involved in the organization of several conferences at Instituto Gulbenkian de Ciência, and there is considerable international visibility. Nationwide, they are extremely active in public health policy making and in (mathematical) biology related public networks, from monitoring the influenza monitoring system Gripenet to coordinating the Lisbon Epidemiology Consortium.

The group publishes many papers and in very good journals (Science, Proc. Nat. Aca. Sci.).

The level of training is very solid.

The Panel understands that one of the reasons that led this group to join CMAF is to have readily access to high level statistical modelling, and the Panel urges the group to invest seriously in the strengthening of the statistical component of their work. Indeed, the group is already expanding into statistics, for example by collecting and analyzing data on influenza. However, the potential for statistical research is higher than this. There are extremely challenging problems, for example, in trying to predict the development of an epidemic from limited observations in its early stages. With the new contact that the group has with statisticians, there is strong potential for development in this kind of direction.
Nonlinear Analysis and Free Boundary Problems [RG-MATH-LVT-Lisboa-209-2397]
This is a very active, albeit small group, and their research is of high quality.

Funding is excellent, mostly FCT awards, although there does not seem to include participation in European projects and/or networks.

The expertise is in free boundary problems, obstacle problems, and problems in continuum mechanics, including elliptic and parabolic equations with non standard growth conditions and variable nonlinearity, with applications to porous media, free boundary problems in biological models (the oxygen consumption problem). Future work will address multiphase constrained diffusion problem, nonlinear PDEs with nonstandard growth conditions, electromagnetism with nonlinear power laws.

The group has excellent visibility and networking, and the productivity is very good, with papers appearing in good journals such as Calc. Var, and PDEs, ESAIM. The coordinator of this group is the Coordinating Editor of the EMS journal on Interfaces and Free Boundaries. This brings prestige and visibility to the group and to the Portuguese mathematics community.

The group has a solid training record and has organized high level conferences in Portugal.
Statistics [RG-MATH-LVT-Lisboa-209-1169]
This work of this group combines several standard statistical techniques, from regression and analysis of variance, to time series and spatial statistics, with a view towards applications in environmental (marine biology, water-quality assessment in river basins, etc) statistics. The research topics cover such themes as estimating trends in time series, and kriging (spatial prediction) and state space models (such as the Kalman filter). These are highly relevant techniques in the context of the applications being discussed. Although being engaged in several public projects, this group has not secured external funding.

The group has contacts with several international researchers mostly in Europe and in Canada, although participation in international conferences is somewhat weak and the research output is also low.

There is a problem with the leadership of this group because the present coordinator has expressed her desire to discontinue this role in view of other scientific and administrative commitments. However the viability of the group depends on senior leadership and the panel does not see any other candidate for that role at the present time. Therefore, the panel recommends one of two courses of action: either the present coordinator finds some way to continue her leadership of the group, or the group as a whole should seek a transfer to some other research centre. The work of the group is too important to be simply discontinued.
Stochastic Analysis, Mahematical Physics and Applications [RG-MATH-LVT-Lisboa-209-1165]
Topics include the study of granular media through variational methods, stochastic semilinear equations, the study of Poisson-Vlaslov equation, and quantum control.

The productivity of this group is excellent, with papers accepted in some of the best journals in the area, such as Arch. Rat. Mech. Anal., Acta Math., J. Funct. Anal. They are very well connected internationally and often are invited to high-profile conferences.

The level of training of this group is somewhat weak; mostly directly to MSc. Long absences of one of its most prolific members prevent this member from actively participating in the training of young researchers.