Page 11 - Textos de Matemática Vol. 44

ON NATA´LIA BEBIANO DA PROVIDEˆNCIA E COSTA’S LEGACY
ALEXANDER KOVACˇEC
Nat´alia Bebiano’s talent and orientation as a mathematician where visible to her peers already before the publication of her Ph.D. thesis [B84] written under the direction of Professor Graciano de Oliveira and the complementary work [B85]. Part of the latter had been published three years earlier, see [B82]. According to these works her primary interests in that time where generalized numerical ranges and permanents.
Since then she has published more than sixty scientific articles with a number of coauthors. The most frequent of these is her father in law, the physicist Jo˜ao de Providˆencia. Some of her doctoral students like Grac¸a Soares, Ruth Lemos, Ana Bezerra Nata continue a close collaboration with Nat´alia (even! ⌣) after their Ph.D. Further students who successfully completed their Ph.D. under her guidance and thus are to be included in the Math’s genealogy project are Ricardo Teixeira, and Cec´ılia Perdig˜ao. Other coauthors include Jo˜ao Queir´o, Yiu-Tung Poon, Jorma Kaarlo Merikoski, Ari Virtanen, Chi Kwong Li, Susana Furtado, Hiroshi Nakazato, Carlos Fonseca and the writer of this survey.
To categorize Nat´alia’s work we would say it centers around the follow- ing topics: extensions of the classical numerical range, in particular numerical ranges defined by indefinite inner products, determinantal ranges and the de Oliveira Marcus Conjecture, and matrix inequalities. Besides, as mentioned, Nat´alia has papers on permanents and a recent one on tridiagonal matrices. Some papers where inspired by questions from statistical mechanics and quan- tum mechanics.
Nat´alia’s interests and imagination are not limited to mathematics. Nat´alia also wrote children’s books and contributed to history and biography of math- ematics in Portugal; last but not least she has entertaining books contributing to the popularization of her science.
We confess the section headings chosen in this survey are somewhat prob- lematic. Studies on numerical and determinantal ranges often are done in the same paper with the purpose to reveal analogues; similarly the work on the de Oliveira Marcus Conjecture is in techniques often related to this work and also to some types of matrix inequalities. This led the present author to opt
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