Barbosa is professor in the Departamento de Matematica, Universidade Federal do Ceara, Campus do PICI, Fortaleza, Brazil. A well known mathematician and expert in differential geometry, he has made outstanding contributions to the stability of minimal immersions of surfaces in the Euclidean space, and towards precise, simple conditions to decide when critical points for the variational problem of minimizing area are minimal. He has been awarded the Medal of Scientific Merit of Brazil, is fellow of the Brazilian Academy of Sciences and of the Academy Cearense of Sciences, and is a member of the Brazilian and American Mathematical Societies and the Brazilian Society for the Progress of Science. He was, for two terms, the president of the Brazilian Mathematical Society. Recently he became Professor Emerito, Universidade Federal do Ceará.