Programa de Financiamento Plurianual - 2007

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Relatório de avaliação

Avaliação de Unidade de I&D
Painel de avaliação, Apreciação global, Financiamentos, Relatórios

Apreciação global

Painel de avaliação
(Matemática) Jean-Pierre Bourguignon, David Cox, Roland Glowinski, Gérard Huet, Thomas Laffey, Jalal Shatah, Carles Simó, Vera T. Sós, Joel Spencer, Tamas Terlaky, Irene Fonseca (Coordinator)

Relatório do painel
The rating of this Center should be read as G+.

This Center was acknowledged in 1996 and in 1999 as housing some of the leading experts in Portugal in partial differential equations and in stochastic analysis. This appreciation still holds.

The research activity is structured along four lines, namely:

1. Differential Equations of Mathematical Physics
2. Probability-Statistics
3. Numerical Analysis of Differential Equations
4. Algebra, Functional Analysis,Topology and Education

Line 1 consists of world class specialists of the mathematical analysis of free boundary problems for partial differential equations of Mathematical Physics, including porous media, Hele-Shaw and nonlinear diffusion problems. The questions addressed are all related to important applications, and from that point of view the panel regrets that this competence is not better exploited by the Portuguese community.

Line 2 is engaged in the study of the behavior of the high frequency end of linear elliptic operators with random elements, and random microstructures related to the transition from micro to macro scale in problems of mathematical physics. Again, the work here is excellent and falls into the mainstream of research in this topic. There are active collaborations between Lines 1 and 2, in particular concerning combustion. The methods developed by this group are mainstream and applicable to many practical problems (e.g. those addressed by Larry Winter at Los Alamos National Laboratories on flow in random porous media).

The work in numerical analysis is exciting. It deals essentially with the numerical solution of some free boundary problems by moving mesh based finite element methods. There is also some work on the numerical
solution of problems from micro-electronics, in cooperation with local electrical engineers. This is a very positive move, and we strongly encourage the multiplication of such collaborations. This area of research seems to suffer from a lack of collaboration with the differential equations group. If this collaboration comes to fruition, then there is room here for a large number of outstanding Master and
PhD theses on the Numerical Analysis of free boundary problems.

In the area of functional analysis there is a young researcher interested in very important problems. Unfortunately, he is very isolated and would greatly benefit from interactions with mathematicians from other centers. To a lesser extent, some research
in statistics and in algebra is also being carried out, the latter targeting the radical theory of associative rings, which differs considerably from the mainstream semigroup theory found in most Portuguese mathematics research centers with an algebra component.

However this Center has clearly outstanding and serious (management) problems to address, in particular:

-- Publications: There is a very low production rate. Research of this high caliber is usually much more productive. Moreover, the international journals where this group elect to publish are not very prominent. Therefore, in addition to making an attempt to increase their rate of publication, these researchers should
publish in more highly regarded journals.

-- Impact in the Portuguese Mathematics Research Community and Networking:
As in 1999, the panel expresses its concern that this wealth of scientific expertise is not having its impact on the Portuguese research community due to the isolation of this Unit, both geographically as well as scientifically. Although the geographical situation of the center may present a barrier in terms of physical mobility of researchers to and from the UBI, nowadays this should not present an overwhelming obstacle to the interchange of ideas and the participation in the national research agenda ((co-)supervision of PhD theses, (co-)mentoring of postdoctoral fellows, organization of workshops, collaborations, etc.).

-- Students:
As mentioned above, the poor networking with the rest of the Portuguese mathematics research enterprise is also reflected on the lackluster training record. Networking with other Centers should enable these high level mathematicians to recruit students and have
quite a positive influence on the development of mathematics in Portugal.

-- Vision:
Throughout the years the Unit has increased in size, but there is a sense of lack of vision and the internal structure that a research center ought to have. As an example, there are no regular seminars (there were held 4 or 5 seminars during the past academic year). This is unacceptable at any research institute. There should be regular seminars where the speakers might be members of the Center reporting on their own work or on other interesting work of interest to the speaker.

-- Funding:
This Center should actively pursue the engagement in networks and European partnerships. Young researchers are not being encouraged to submit individual proposals (actually, senior members do not seem to be much aware of the FCT award mechanisms, again a another strong indication of the isolation of this group).

-- Presentation:
The panel recommends more care both in the oral as well as in the written presentations of the research work of the unit. The written report was not informative. Not only its body was written in Portuguese, what presented a serious impediment to panel members, as
it repeated, in a summarized way, what was essentially already included in the report of 1999.

To be noted, the situation of senior members is very precarious: after several years in the country they still do not hold a permanent position, and are employed under contract renewed on a yearly basis. This is not of much help either, and it may have influenced negatively students who could have otherwise choose these researchers to be their PhD advisors.

In view of all these comments, the panel recommends that this Center should be funded for one more cycle of three years, under the condition that if no major changes occur to address the concerns expressed above, then the Center should be disbanded and active members should joint other centers where there is a critical mass of researchers with a strong intersection with their programs and potentially strong groups of trainees. This would be a better use of intellectual as well as financial capital.

Comentário da unidade
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