Marcelo Trindade: Ph.D. in Applied Mathematics at the University of Porto

My name is Marcelo da Silva Trindade and I now have a position in Brazil as Professor of Mathematics. I completed my Ph.D. in Applied Mathematics at the University of Porto in 2017. During my Ph.D. studies I was member of the CMUP – Center of Mathematics of the University of Porto – evaluated as excellent by the FCT – Fundação para a Ciência e a Tecnologia – which is the Portuguese public agency that supports science, technology and innovation under the responsibility of the Ministry for Science, Technology and Higher Education.

Portugal has a unique history and is one of the oldest countries in Europe, with the same frontiers since 1143! Can you imagine that? Porto city is located along the Douro river in Northern Portugal and its historical core was proclaimed a World Heritage Site by UNESCO in 1996. The city urban’s area extends to the coastline of the Atlantic Ocean. The University of Porto is well known for the high quality education and for the scientific international reputation, showing the richest academic community in Portugal.

Jointly with my supervisors, Paulo B. Vasconcelos and José Matos, my domain of research was Numerical Analysis, specifically in spectral numerical methods for the solution of integro-differential problems. The Lanczos Tau method was the focus of my thesis dissertation. We developed several contributions for the stabilization of the method, using orthogonal polynomials in the operational formulation. Moreover, we developed a MATLAB toolbox, the TauToolbox, to apply the Tau method to several types of integral and differential problems: ranging from linear differential equations to systems of non-linear integro-differential equations.  As an example, from TauToolbox we have the Lorenz’ attractor easily achieved with high accuracy:

The work was been presented in some international scientific meetings, namely at the 14th International Conference on Integral Methods in Science and Engineering (IMSE 2016, University of Padova, Italy), at the New Directions in Numerical Computation (NDNC 2015, University of Oxford, UK), at the 3rd International Conference on Numerical and Symbolic Computation: Developments and Applications (SYMCOMP 2017, Guimarães, Portugal) and at the 2nd Advanced School on Integral Equations and Applications (IST, Lisbon, Portugal). As a result of my research project two papers and one book chapter were published.

To be at the University of Porto as a Ph.D. student and belonging to CMUP made me greatly improve my knowledge. The excellence of the institution and my supervisors as well, led me the wish to continue to do research in this same area.

Besides that, Portugal will always be in my heart, for the four years living there, for the wonderful and competent people met there, and also for my daughter that was born in the marvelous city of Porto.

University of Porto, hope to revisit you soon!
Marcelo Trindade