CMAFcIO is a R&D Unit engaged in research in Mathematical Sciences, covering domains that range from foundations to applications. Its main objectives are to pursue deep studies in areas of mathematics, to train young researchers at several stages of their career, and to foster and develop applications to relevant problems in the Sciences and from Industry. Along with dissemination of scientific results, the unit promotes the communication of mathematics in schools and for the wider public.


This R&D Unit is the result of a merge, effective since 2015, of the previous Units CMAF and CIO. The new Unit maintained the ranking “Excellent” in the last FCT’s 2013 evaluation which was a confirmation of the previous “Excellent” of the two former Units.

This Unit has a Directive Board of 3 members, an international Advisory Committee, 59 integrated members (including 4 FCT Researchers and 6 Post-Docs), 15 PhD Students and 41 non-integrated members. Members are from the ULisboa (mainly from Ciências, a few from ISEG, Técnico and ISA) and from schools in Faro, Setúbal, Leiria and Coimbra.


We group the significant contributions of the unit into three areas of research:





(1) includes active researchers with a significant international visibility, working in Proof Theory, Model Theory and Combination of Logic, as well as in Geometry, namely Willmore surfaces, D-Modules, Algebraic Geometry, and discrete and continuous Dynamical Systems.

(2) includes one of the largest and strongest group in Portugal in Differential Equations – Ordinary and Partial Differential Equations – with expertise in Calculus of Variations and several applications in Mathematical Physics and in Biomathematics. Relevant topics are the study of specific equations, such as Navier-Stokes, Schrödinger and Kac-Boltzman, together with Kepler-type problems, functional-differential equations, kinetic theory of gases, phase field models, elasto-plasticity, free boundary problems, shape optimisation, renormalisation and signal processing.

(3) includes researchers from a pioneer group in Portugal whose scientific production in Discrete and Network Optimisation is considered a reference at international level. Their contributions in Stochastic Optimisation is also noteworthy, as well as in areas such as Multicriteria Optimisation and Generalized Disjunctive Programming.

Some of the research done by members of this unit, namely from areas (2) and (3), can be filed under APPLIED AND INDUSTRIAL MATHEMATICS. The increased visibility of this field in the unit is a consequence of the merge of two former units. Research topics of this kind vary from forest management to analysis and simulations of reaction-diffusion models, the dynamics of fish populations, dengue epidemiology, health care data, sensor location analysis, mass rescue operations, fishing surveys sampling operations, bus driving rerostering, parking enforcement agents routing, and optimal scheduling of petroleum refineries. Examples of partners in Industry are Portuguese Navy, EMEL (Mobility and Parking in Lisbon), IPMA (Sea and Atmosphere Institute), ABB, SASOL, Unilever, and several public and private hospitals.


The international visibility of CMAFcIO can be seen in several other aspects that result from the active research of its members: i) journal Editorial Boards, ii) membership and leadership in international research groups and scientific organizations, iii) chairing and organization of international conferences and schools, iv) collaborations with many researchers from abroad.