Profile

After completing undergraduate degrees in Mathematics at the University of Porto (1976, 1978), I pursued graduate studies also in Mathematics at the Universities of Michigan (M.Sc., 1980) and Penn State (Ph.D., 1982). I was a post-doctoral fellow at Simon Fraser University (1982-84) and returned to Portugal in 1984 as a professor: first, auxiliary at the University of Minho, then associate (1987) and full (since 1991) at the University of Porto. I have visited numerous foreign universities, especially during sabbatical leaves (90-91: São Paulo, Brazil; 97-98: Hobart, Australia; 04-05: Paris VII, France, and Ural State, Russia; 11-12: Masaryk, Czech Republic, and Bordeaux, France; 18-19: again at Masaryk).

My main scientific contribution so far is the development of profinite methods in the theory of finite semigroups, whose main motivation comes from the numerous applications of automata and formal languages in Computer Science. A rich algebraic topological structure comes thus into play in the study of useful but structurally poor models. In particular, decidability questions, which are central in the applications, lead to natural classical mathematical problems such as word problems and topological separation or denseness in a suitable solution space of equation systems. I also found and explored remarkable connections between profinite semigroups and symbolic dynamics that both shed light on the structure of free profinite semigroups and provide new invariants for symbolic dynamical systems.

In recognition of my research achievements and career, I was decorated by the President of the Portuguese Republic as Commander of the Military Order of St. James of the Sword (2000, on the occasion of the International Year of Mathematics), and elected honorary member of the Portuguese Mathematical Society (2022).