MEETING ON LINEAR ALGEBRA AND APPLICATIONS

September 8-10, 2003

Universidade Nova de Lisboa, Caparica, Portugal
(on the occasion of Graciano de Oliveira's 65th birthday)

 

 

After-dinner speech, September 9

João Filipe Queiró

 

 

I was asked to say a few words as a toast to Professor Graciano de Oliveira.

 

Graciano de Oliveira of course does not need an introduction. Practically everyone here knows him. Many of us, even if some don’t know it, do our research work under his influence. It may be a distant influence, but it is certainly there: on eigenvalues and singular values, on completion problems and inverse problems, on invariant polynomials and control theory, on multilinear algebra and preserver problems. Many lines of research that we now see very active in Portugal, in Spain and in other countries have their roots in papers Graciano de Oliveira wrote in the 60s, 70s and 80s.

 

I was a witness to Graciano de Oliveira’s second wave of student inspiration (the first, in the early 70s, led to the beginning of the research career of José Perdigão Dias da Silva and Eduardo Marques de Sá). This was in Coimbra in the late 70s and early 80s. I still remember very well the constant seminars, the regular visiting by famous people, the lists of open problems circulating. And I remember even better Graciano de Oliveira’s style of questions: Why don’t you try normal instead of Hermitian?… Permanent instead of determinant?… F instead of C?… And the worst of all: What are you doing here? When will you write your first paper? Why don’t you write more papers?

 

Sometimes we had our doubts, and asked silly questions, such as: What is this good for? Is there any application for this? And the answer was immediate: Of course it is applied mathematics, you can apply it to writing a thesis. It seems a joke, but there was a lesson in this: if you worked hard, if you thought about mathematical problems, you would be training your mind. Afterwards – after writing your thesis – you could apply this training to whatever you wanted, pure or applied.

 

And I should point out that, even if the suggestions seemed quite arbitrary, there was, most of the time, very good mathematical taste in the subjects studied in the seminars and in the problems suggested. For example, the Horn and Mirsky papers of the 50s and 60s on eigenvalues, singular values and diagonal elements. Or Horn’s famous paper on eigenvalues of sums of Hermitian matrices. These are papers that have had a great influence and have been studied and generalized by many people in deep settings.

 

The constant questioning also illustrates another feature of Graciano de Oliveira, which is his love for conversation, for argument, even for provocation. I am sure many of you have had first-hand experience of this. Graciano de Oliveira loves to provoke you, to argue with you, to find fault in your logic. If you are not very sure of yourself, he will easily win over you in a logical argument. And he likes logical jokes. As an example, I recall the visit of a famous mathematician, who had something peculiar about his eyes. Someone said: “Did you notice? The whites of his eyes are blue.” Graciano de Oliveira immediately replied: “That’s nothing. I know lots of people for whom the blues of the eyes are white.”

 

Anyway, the good thing is that we all, who lost so many arguments with him, will have many years to try and think of new, better answers to Graciano de Oliveira’s questions, and to think about the mathematical problems for which, directly or indirectly, he was the inspiration.