The Mathematical Analysis Group at CMUC conducts research at the interface of several core areas of modern analysis. Its main interests include partial differential equations - with a strong focus on regularity theory and free boundary problems - the theory of function spaces, with emphasis on sharp embeddings, and orthogonal polynomials, particularly in connection with Riemann-Hilbert problems, Markov chains, and integrable systems. The group's research is published in leading international journals, and its members are authors of influential books and monographs that help shape the state of the art in these fields.

As a dynamic and internationally connected team, the group has been consistently successful in securing competitive funding at both national and international levels. It offers a stimulating and rigorous environment for doctoral students and postdoctoral researchers, many of whom now hold prominent positions in academia and industry in Portugal and abroad. The group is also actively engaged in the organisation of conferences and thematic programmes, editorial activities, and outreach initiatives, contributing to a vibrant and growing mathematical community in Coimbra.