R&D Institutions

Resultado da avaliação 2007 na área de Matemática

Unidade de I&D

Centro de Estruturas Lineares e Combinatórias [MATH-LVT-Lisboa-1431] visitada em 20/02/2008

Classificação: Very Good

Comentários do painel de avaliação
Sobre a unidade
The unit is very strong in linear algebra, an area which has traditionally flourished in Portugal. Several members of the unit are recognized as world leaders in this field. Recently the unit has diversified its interests, and this is a welcome development. There is a clear criterion for membership in the unit. The focus of the unit's research is a set of classical and hard problems in linear algebra, and they continue to make progress on these problems. In their work they deploy a wide range of techniques with great ingenuity.
The panel suggests that in the next evaluation the unit should give more careful attention to the preparation of the unit report and the group reports. In some respects they were unclear, and the panel would have welcomed more detail on some points. In particular the requests for programmatic funding under the heading of "Special requests" in each group report were confusing, to the extent that the panel struggled with the recommendation for programmatic funding.
The panel did not understand the rationale for the division into groups given in the unit report. Group 1 works in many different areas. Groups 2, 4, and 5 work in closely related areas. It is questionable whether the work of the combinatorics group (3) is focused in combinatorics, since for example most of their papers appear in algebra journals. The overlap between the several groups is very large.
The unit would benefit from further broadening of its interests. While the panel understands that the journal "Linear algebra and applications" is the recognized outlet for work of high quality in linear algebra, the unit would benefit in terms of visibility and recognition by publishing in a wider range of journals. The unit works mostly in an area which has wide applications, but the panel felt there was limited interest in or knowledge of the relevant applications among the researchers in the unit. There could be more international collaboration, a more aggressive search for funding external to FCT, and more participation in the wider world of European mathematics. The unit would benefit from reflecting on its long-term strategy.
The unit participates in several outreach activities. The panel especially commends the activities in secondary school education.

For the purposes of ranking and programmatic funding, the panel divided the personnel of the unit into two disjoint sets, following as far as possible the lines of the division made by the unit in the report. The panel used the list of personnel from the unit's web page at the URLhttp://celc.cii.fc.ul.pt/elc/nomes/index.htm

Group I: (groups, fields, combinatorics, commutative algebra, cellular automata)

Ana Luísa Rodrigues Branco Correia
Carlos Alberto Martins André
Joaquim Eurico Anes Duarte Nogueira
Ana Margarida Palma de Carvalho Neto Castro Tavares
Owen John Brison
Pedro Jorge Santos Freitas
Ilda Perez Fernandez da Silva

This set of researchers works in a range of areas including commutative algebra, representation theory, cellular automata and combinatorics. The scientific level varies from good to very good, and their work has appeared in a variety of journals including some very good ones. The panel ranked this set of researchers in the middle of the very good range.
This set of researchers has some international connections and collaborations with researchers (some of them very well known) in Brazil, Spain, France and the USA. They have organized some international summer schools in algebra.
Members of this set of researchers have trained several PhDs, many of whom have been integrated into the unit.

Group II (matrix theory and multilinear algebra)

Fernando Abel Conceição Silva
Gloria Maria da Silva Pereira Cravo
Henrique José Freitas da Cruz
Isabel Maria Teixeira de Matos
Jose Antonio Perdigao Dias da Silva
Laura Cristina Teixeira Iglésias Charters de Azevedo
Maria Antonia Duffner Bessa Monteiro
Maria da Purificacao Antunes Coelho
Maria de Fátima Vale de Gato Santos Rodrigues
Maria do Rosario Silva Franco Fernandes
Maria Manuel Correia Torres
Marija Dodig
Susana Margarida Figueiredo de Sousa Borges Furtado
Isabel Cabral
M Isabel Faria
Cristina Ferreira
M Amélia Fonseca
M Graça Marques
Rita Simões
Enide Andrade Martins

This set of researchers works in linear algebra, primarily matrix theory and multilinear algebra. They are acknowledged experts in this area. They are quite productive, and publish almost exclusively in one or two specialist journals. In matrix theory they mostly work on completion problems, matrix stability, problems involving similarity and congruence, and non-negative matrices. In multilinear algebra they mostly work on equality, decomposition, preservation and conversion of tensors. This set of researchers is the dominant group in the unit, and the panel ranked them as very good.

This set of researchers has international connections and collaborations with well-known researchers, and would profit from strengthening their international ties.
They have organized an international meeting in linear algebra.

Members of this set of researchers have trained quite a number of PhD's, many of whom have been integrated into the unit. They would benefit by making an effort to attract researchers who were trained elsewhere, and by sending out their trainees for postdoctoral training in other groups. The panel recommends that they continue and strengthen their efforts in the direction of working on problems from engineering, and should also consider similar initiatives for the many other disciplines in which linear algebra is an essential tool. They could also look at linear algebra from a more computational point of view.

Sobre os grupos de investigação
Abstract Algebra [RG-MATH-LVT-Lisboa-1431-1521]
Applied Linear Algebra [RG-MATH-LVT-Lisboa-1431-1522]
Combinatorics [RG-MATH-LVT-Lisboa-1431-1523]
Matrix Theory [RG-MATH-LVT-Lisboa-1431-1524]
Multilinear Algebra [RG-MATH-LVT-Lisboa-1431-1525]