R&D Institutions

Resultado da avaliação 2007 na área de Matemática

Unidade de I&D

Centro de Matemática da Universidade de Coimbra [MATH-Centro-Coimbra-324] visitada em 22/07/2008

Classificação: Excellent

Comentários do painel de avaliação
Sobre a unidade
CMUC is a large center, with 56 FTE members.
It has considerable strengths in both fundamental and applied mathematics. It has developed a leading role in Portugal for computational mathematics.
The panel was impressed by the excellent presentation of the unit and of the individual teams. The leadership of the center came out as both energetic and thoughtful, continuing and expanding a long-running effort to bring the research of the center to the highest level.
The recently approved PhD program (joint with researchers at the University of Porto) has completed one year and currently has approximately 40 students enrolled. We applaud the effort to establish high standards for the program, the inclusion of foreign students into the program, and encourage current efforts to increase the number of Portuguese students.
The center is composed of 6 groups. In addition to the activities of the groups, it has a remarkable outreach activity, including communication towards high-school students and an important involvement in the organization of the Mathematics Olympiads.
The panel noted a potential for interaction between the analysis and the numerical analysis group.
Sobre os grupos de investigação
Algebra and Combinatorics [RG-MATH-Centro-Coimbra-324-1221]
The group is quite large, with 11 PhD members and 9 members without PhD. It has obtained projects funding from the FCT and from the Gulbenkian Foundation. It has supervised 5 PhD theses and 16 Master theses between 2003 and 2006.
It has a leading position in Portugal in linear algebra. It has interesting activities concerning the spectral analysis of hermitian matrices and of matrices associated to graphs, as well as in combinatorial questions involving linear algebra. Some of its members have achieved high international visibility in their field. The group has published many papers in international journals, with a strong concentration in two journals.
The panel welcomes the group's recent diversification into new areas, linking combinatorics to matrix theory and Banach algebras.
Algebra, Logic and Topology [RG-MATH-Centro-Coimbra-324-1245]
This is a large group, with 13 PhD members and 2 members without PhD. It has received project funding from the FCT as well as from the EU (INTAS program).
The group is active in category theory, more specifically in algebraic and categorical methods in topology and logic. The level of productivity is quite variable; several members of the group are quite productive and/or have a strong international visibility. Some papers have been published in the leading journals of the area (one paper, at the beginning of the period, has been published in one of most selective mathematical journals). Some of the work of the group has been influential in its field.
The panel welcomes the group's intention to develop the potential relations with domain theory and more generally with computer science.
The group has trained five PhDs in the review period, several of whom were absorbed into the group.
The publication record of those PhD students is varying.
The group has been energetic in organizing conferences, and has several international collaborations.
Analysis [RG-MATH-Centro-Coimbra-324-1222]
This is a large group, with 12 members with PhD and 2 without PhD.
The group has received some projects funding from the FCT, as well as important funding from several different EU programs. It has supervised 3 PhD thesis and 5 Master theses in the period 2003-07.
The activities of the group go from theoretical aspects of analysis and PDE to applications. It has a focused set of overlapping research projects being addressed by different researchers. Some members of the group have achieved high international recognition, with publications in the leading journals of their area.
This group is very strong in the areas of analysis and PDEs. Work includes very contemporary topics in nonlinear PDEs with relevance in porous media, composite materials, financial markets, PDEs with variable exponents suited for imaging, electrorheological fluids, modeling of bone, piezoelectric materials, thin structures, nonlinear reaction diffusion equations within the context of nonlinear elasticity, non-Newtonian fluids, etc. The group has made major contributions in regularity theory for singular and degenerate PDEs, in the study of Boltzmann- type kinetic equations, p-Laplacian, etc. The publication record is excellent. Papers are published is some of the top journals, and jointly with top researchers.
The panel was particularly interested in the applications to biology, which are both mathematically interesting and of real value for important applications. The panel hopes that this activity will lead to publications in first-rate biomedical or engineering journals in the near future.
The group has strong international link with first-rate teams, in particular with the University of Texas at Austin in the framework of the UT Austin | Portugal program.
Geometry and Applications [RG-MATH-Centro-Coimbra-324-1244]
The Geometry and Applications group is rather large, with 6 members with PhD and 5 members without PhD. It has obtained some projects funding from the FCT and from the French embassy in Portugal.
Some of the members of the group appear to have a strong research activity with a good international visibility, and they publish regularly in renowned international journals of the area. This mostly concerns mathematical physics, in particular the study of Lie algebroids and Poisson geometry. However the group might be even more ambitious in its endeavors and concentrate more on the main questions in the area.
The results obtained in low-dimensional topology are very interesting but journal publications in this area are still lacking.
Numerical Analysis, Optimization and Applications [RG-MATH-Centro-Coimbra-324-1242]
This is a large group, with 8 PhD members and 5 members without PhD.
The group has received projects funding from the FCT, as well as from the EU and from the European Space Agency.
The group has a strong activity in the area of numerical analysis, optimization, and computational mathematics, and has published several papers in the most renowned journals of this field. Some members of the team have strong activities related to applications.
The group has a very good choice of main topics: Reaction-Diffusion, Navier-Stokes equations and development of industrial software, Super and Supra-Convergence analysis, Volterra integro-differential equations in Fickian models, High-Performance Nonlinear programming software, Non-differentiable Optimization, Nonstationary Markovian service systems.

Among the strong points, the panel noted the interdisciplinary collaborations and the focus on extensive scientific computation.
The group has obtained very good results: new splitting numerical methods, vorticity boundary conditions for Navier-Stokes equations, interesting application to Pulp and Paper Industry, clever use of Volterra integro-differential equations, new concepts in optimization, new methods for accurate sampling, interesting applications to nonstationary queues.
It has a very good productivity, with publications in high quality international journals in numerical analysis/optimization/operational research.
The members of the group have very good visibility at international level, including collaborations with many prestigious foreign centers and participation in editorial boards.
Probability and Statistics [RG-MATH-Centro-Coimbra-324-1243]
This is a smaller group, with 4 members with PhD, one without PhD, and
2 associate members. It puts forward a diverse proposal with several themes:
(a) empirical process theory in the dependent case; (b) asymptotic properties of density estimators based on empirically chosen kernels; (c) Bayesian methods for human genetics. The panel hopes that directions (a) and (b) will need to strong contacts with the applications in the near future.
The group has produced numerous publications in respected journals, e.g. the Journal of Nonparametric Statistics, Statistics and Probability Letters. It has a strong emphasis on positive dependence, and is encouraged to develop new directions.
One PhD student member of the group is part of an excellent team at Oxford University and participates in top-level research by a big consortium. This research direction appears new to the country and should be strongly encouraged. The heavy computational emphasis in this type of inference sits well in the general direction taken by applied mathematics at Coimbra, and complements the other statistics activities well.