FCT

R&D Institutions

Resultado da avaliação 2007 na área de Matemática

Unidade de I&D

Centro de Matemática da Universidade do Porto [MATH-Norte-Porto-144] visitada em 21/07/2008

Classificação: Excellent

Comentários do painel de avaliação
Sobre a unidade
This is a large research unit with 58 Ph.Ds, 20 Ph.D. students, and 13 Postdocs that is organized into 8 research groups that cover a broad range of pure and applied mathematics much of which is at high international standards. The recently approved PhD program (joint with researchers at the University of Coimbra) 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 fact that the unit both includes all the research efforts of the mathematicians at Porto while maintaining minimal standards for full membership within the institute eliminates artificial barriers, encourages collaborations, and provides breadth of opportunities for the graduate students and postdocs.

The panel is impressed by the breadth, organization, and apparent quality of outreach efforts including, but not limited to, the development of mathematical consulting services, outreach to secondary schools, cooperation with cultural institutions, and mathematical history. The panel is strongly supportive of the unit's plan for Future Networking activities. However, given the strengths of this unit we encourage an even more aggressive plan. The plan by the Geometry and Topology group to strengthen the international visibility of Mathematical Physics in Portugal in cooperation with CFP, CMA (IST), and Algarve through visiting and travel programs should be supported. Similarly, the Dynamical Systems group at CMUP complements other strong dynamical systems groups in Portugal, in particular that of IST, and a well coordinated network would make Portugal one of the European leaders in dynamical systems and presumably position the Portuguese researchers to successfully compete for large EU funding.
Sobre os grupos de investigação
Algebra, Combinatorics and Number Theory [RG-MATH-Norte-Porto-144-697]
This medium sized group which includes 7 PhDs intends to conduct research on a variety of topics including: quantum groups, ring theory, Lie theory, Hopf algebras, number theory and cryptography, matroid theory, enumerative combinatorics and computational geometry. This program provides needed breadth to the Portuguese efforts in the areas of algebra combinatorics and number theory. The past work of this group is solid both in terms of the number of publications and in the quality of publications. The educational efforts are mixed; a large number (21) of MSc theses were supervised from 2003-2007, but only one PhD was granted.
Analysis [RG-MATH-Norte-Porto-144-698]
This medium sized group which includes 7 PhDs intends to conduct research on a variety of topics including: dynamics and control of satellites, models of plastic surgery, orthogonal polynomials, econophysics, special functions, integral transforms, summation formulas, magnetohydrodynamics, and shocks. While this group has supervised a substantial number of students, (8) MSc and (4) PhD, and produced a substantial number of papers, the panel questions the quality of this work, or at least its impact on the visibility of Portuguese mathematics. The publications are not in the leading international journals. Furthermore, there is little sense of unity to the proposed projects, thus an impact can only come through exceptional results. The likeliness of this is diminished by the fact that as described in the research proposal these topics are classical and/or narrow.
Dynamical Systems. [RG-MATH-Norte-Porto-144-702]
This medium sized group which includes 19 PhDs intends to conduct research on a broad range of disciplinary topics: ergodic theory, low dimensional dynamics, bifurcation theory, singularity theory, and topological dynamics. Furthermore, their work intersects with that of other mathematical disciplines such as geometry, topology, probability and statistics. Finally, they are involved in applications in economics, biology and hydrography. Given the size of the group it is not surprising that there are disparities in the research productivity of the members, however there are several researchers that have achieved strong international recognition with regular publications in the top theoretical and applied journals. This strength is also reflected in the various additional national funding for individual research projects that have been obtained.

The educational efforts are strong; they have and through the Ciência program will continue to mentor a solid number of postdocs, a large number (24) of MSc theses were supervised from 2003-2006, along with a substantial number (6) of PhDs. The group has also been active in the organization of conferences, workshops, summer schools and networks on a national and European level.

The committee remarks that given the breadth and depth of dynamical systems in Portugal a more coordinated national network coupled with more aggressive pursuit of large scale EU funding could result in Portugal assuming a leading international role in this broad area of pure and applied mathematics.
Geometry and Topology [RG-MATH-Norte-Porto-144-700]
This medium sized group which includes 7 PhDs intends to conduct research on a variety of topics including: mathematical physics, moduli spaces of surface group representations (including Higgs bundle methods), differential and algebraic geometry, Poisson and symplectic geometry, singularity theory, differential equations and control theory. Most of its members are internationally recognized mathematicians, some of whom have published in recent years in the best mathematical journals and all have at some point published in well recognized journals. The educational efforts are strong; they are and through the Ciência program will be mentoring a large number of postdocs (8), a large number (15) of MSc theses were supervised from 2003-2006. Only one PhD was granted during this time period which is a shame given the strength and timeliness of the work of this group. This group has also been active in the organization of conferences, workshops, summer schools and networks on a national and European level. These efforts have been supported in part by external funding. The panel encourages this group to continue their leadership in this important and prominent area of mathematics and to continue to seek funding opportunities on the level of the EU.
History and Mathematics Education [RG-MATH-Norte-Porto-144-701]
Numerical Analysis, Probability and Statistics [RG-MATH-Norte-Porto-144-699]
This group consists of two distinct research groups that of Numerical Analysis and that of Probability and Statistics. This group of 7 PhDs has supervised a substantial number of students, (8) MSc and (4) PhD. As a group there appears to be a tremendous effort in the organization of conferences, to the extent that it may be conflicting with the production of quality research. The panel notes that within statistics few papers have been published, though one will appear in an excellent journal. Within numerical analysis there are greater number of publications appearing in reputable journals, but they seem to have generated little impact in terms of citations. It is also noted that software has been produced, though again there is no indication of its impact or use by other groups.

The proposed research topics- Eigenvectors of quasi-diagonal matrices, Integral Fredholm operator equations with weakly singular kernels, Absorption of photons in stellar atmosphere, Tau-method, Frobenius-Padé approximants, software development, Estimation of tail indices, Re-sampling methods - are appropriate given the expertise of the group and appear to be attainable. However, given the lack of overlap between the research programs of numerical analysis and probability and statistics, the panel suggests that the group consider reorganizing.
Semigroups, Automata and Languages [RG-MATH-Norte-Porto-144-703]
This small group which includes 4 PhDs intends to conduct research on a variety of topics including: group theory, geometry of monoids and actions, profinite semigroups, and numerical semigroups. All the members of this group are strong and active, with some being recognized as international leaders having substantial impact on the directions of the field as a whole. Given the size of the group, the educational impact is substantial: 9 MSc theses, 2 PhD theses and the mentoring of postdocs. In addition there is substantial international contacts and networking ranging from conferences to research projects to software development.
Signal Processing and Data Analysis [RG-MATH-Norte-Porto-144-704]
This small group which includes 4 PhDs intends to conduct research on a variety of topics: biomedical signals and systems, statistical modelling in health sciences, bioinformatics, and statistical learning. As a group there is a substantial level of publications in internationally recognized journals and conference proceedings, however there is an uneven level of activity by the group members. The group has numerous supported research projects, both nationally and internationally. Given the size of the group, the educational impact is significant: 11 MSc theses, 3 PhD theses and the mentoring of postdocs.