2020/2021 edition

2020/2021 (5th edition) is at University of Porto


Tuesday, 22th December 16:00
Optimal Control Problems Arising in Drone Missions for Disaster Search and Rescue Operations

Fernando Lobo Pereira, SYSTEC, Faculdade de Engenharia da Universidade do Porto

Wednesday, 16th December 12:00
Conceptual Analysis of Complex Data

Paula Brito, Faculdade de Economia da Universidade do Porto e LIADD

Wednesday, 16th December 11:00
Distributions, the “number of the future”

Sónia Dias,  IPVC  e LIADD; Paula Brito, Faculdade de Economia da Universidade do Porto e LIADD

Wednesday, 9th December 12:00
Harnack Inequalities for Nonlinear PDEs
Eurica Henriques, CMAT

Wednesday, 9th December 11:00
A new call-by-value λ-calculus based on natural deduction with general elimination rules
José Espírito Santo, Universidade do Minho e CMAT

Wednesday, 2nd December 11:00
A kinetic model of T cell autoreactivity in autoimmune diseases
Maria da Piedade Machado Ramos, Universidade do Minho e CMAT

Wednesday, 25th November 11:00
An introduction to variational and quasivariational inequalities
Lisa Santos, Universidade do Minho e CMAT

Wednesday, 18th November 11:00
From theory to practice: applying the fundamentals and tools of scientific computing to an existing project
José Abilio de MatosFaculdade de Economia da Universidade do Porto e CMUP

Wednesday, 11th November 11:00
Deep learning on the search of new physics
Felipe Ferreira de Freitas, Departamento de Física  & CIDMA, Universidade de Aveiro

Wednesday, 4th November 11:00
Emergence of strange attractors from singularities
Alexandre Rodrigues, Departamento de Matemática & CMUP, Universidade do Porto

Wednesday, 28th October 11:00
Mathematical modeling, optimal control and complex network of epidemic models
Cristiana Silva, Departamento de Matemática & CIDMA, Universidade de Aveiro

Wednesday, 21th October 11:00
Evolving Social Networks: trajectories of communities
João Gama, Faculdade de Economia da Universidade do Porto & LIADD- INESCTEC

Wednesday, 14th October 11:45 am 
Fit of immune response by CD4++T cells triggered by LCMV infection

PhD Scholarships

Opportunities for the academic year 2023/2024

Call from the Centre of Mathematics of the University of Minho (CMAT): June 20th 2023 — July 4th 2023, 23:59h (Europe/Lisbon).

Call from the Mathematics Center of the University of Porto (CMUP): June 5th 2023 — June 26th 2023 by 23h59 (GMT+1, Lisbon time).

Opportunities for the academic year 2022/2023

Call from the Mathematics Center of the University of Porto (CMUP): July 28th 2022 — August 10th 2022 by 23h00 (GMT+1, Lisbon time).

Call from the Mathematics Center of the University of Porto (CMUP): July 1st 2022 — July 14th 2022 by 23h59 (GMT+1, Lisbon time).

Call from the Centre of Mathematics of the University of Minho (CMAT): June 23rd 2022 — July 15th 2022, 23:00h (Lisbon time zone).

Call from the Mathematics Center of the University of Porto (CMUP): April 8th 2022 — May 2nd 2022 by 23h59 (GMT+1, Lisbon time).

Opportunities for the academic year 2021/2022

Call from the Mathematics Center of the University of Porto (CMUP): May 4th 2021 — May 25th 2021 by 23h59 (GMT+1, Lisbon time).

Call from the Center for Research and Development in Mathematics and Applications (CIDMA): June 9th 2021 — July 25th 2021 by 23h59 (GMT+1, Lisbon time).

Call from the Centre of Mathematics of the University of Minho (CMAT): July 1st 2021 — July 16th 2021 by 17h00 (GMT+1, Lisbon time).

Call from the Mathematics Center of the University of Porto (CMUP): July 28th 2021 — August 10th 2021 by 23h59 (GMT+1, Lisbon time).

Call from the Centre of Mathematics of the University of Minho (CMAT): August 4th 2021 — August 17th 2021 by 23h59m (GMT+1, Lisbon time).

2019 / 2020 edition


Dynamic Logics On-demand?
Alexandre Madeira (CIDMA-UA)
December 10, 16:00-17:00

Research themes in Logic
José Carlos Espírito Santo (CMAT-UM)
December 10, 15:00-16:00

On regression tree models for longitudinal data
Cecília Castro (CMAT-UM)
December 3, 15:00-16:00

Hyperplane arrangements and parking functions
Rui Duarte (CIDMA-UA)
December 3, 14:00-15:00

Mathematical modelling of autoimmunity
Maria Piedade Ramos (CMAT-UM)
November 26, 15:00-16:00

Multivariate Analysis of Distributional Data
Maria Paula Brito (LIAAD-UP)
November 26, 14:00-15:00

An introduction to variational and quasivariational inequalities
Lisa Santos (CMAT-UM)
November 19, 16:00-17:00

Coupled cell networks: patterns of synchrony
Manuela Aguiar (CMUP-UP)
November 19, 15:00-16:00

Equations in quaternions
Maria Irene Falcão (CMAT-UM)
November 12, 15:00-16:00

Large scale flows and multiscale techniques
Sílvio Gama (CMUP-UP)
November 12, 14:00-15:00

Problems on numerical semigroups
Manuel Delgado (CMUP-UP)
November 6, 12:00-13:00

Nonlinear evolutionary equations
Eurica Henriques (CMAT-UTAD)
November 6, 11:00-12:00

Modeling with stochastic differential equations
Paula Milheiro Oliveira (CMUP-UP)
October 29, 15:00-16:00

Corruption cycles in democracy
Alberto Pinto (LIAAD-UP)
October 22, 15:00-16:00

Applications of generalized inverses of matrices
Pedro Patrício (CMAT-UM)
October 15, 2019, 15:00-16:00

Some mathematical problems in the kinetic theory for mixtures
Ana Jacinta Soares (CMAT-UM)
October 8, 2019, 11:00-12:00

Academic Calendar

from 3rd of June to 31st of August, 2019

6th of September, 2019

from 30th of September to 2nd of October, 2019


First semester: 4th of October, 2019 — 1st of February, 2020  

Second semester: 3rd of February, 2020 — 20th of June, 2020

2017/2018 edition

Results of the evaluation of candidates

Phase 1

Information about acceptance of candidates to MAP-PDMA and grant recipients (first two) of Phase 1 can be consulted in this file.

Grants evaluation guide Edital 2017

Phase 2


Information about acceptance of candidates to MAP-PDMA and grant recipients (first two) of Phase 2 can be consulted AcceptanceCandidatesFCT2016_2afase.

Phase 3

Information about acceptance of candidates to MAP-PDMA and grant recipients (first two) of Phase 3 can be consulted Ata2017-3afase_assinado

2016 / 2017 edition

Results of the evaluation of candidates

Information about acceptance of candidates to MAP-PDMA and grant recipients (first six) can be consulted  in this file.

The candidates graded with less then 2 points (out of 5) were not admitted to the program. The ranking list is provisional.

Grants evaluation guide Edital2016.

Academic Calendar

Academic Calendar


from 1st of June to 28th of August, 2016

6th of September, 2016

Beginning of the 1st semester – 26th of September, 2016
Results of the 1st semester –  28th of February, 2016
Beginning of the 2nd semester – 13th of February, 2017
Results of the 2nd semester –  29th of July, 2017


1st Year

Advanced Topics in Algebra, Logic and Computacion (ALC)

Three of the following topics are taught each year: Computer algebra: introduction to some computer algebra system; development of topics in computational number theory or in computational group theory. Automata, languages, and semigroups: regular languages; recognizability by finite state automata and by semigroups; (option 1) varieties of semigroups and languages, Eilenberg's theorem; (option 2) Chomsky's hierarchy, decidability problems. Algebraic logic: elements of universal algebra; algebraization of classical, intuitionistic and modal logics; abstract algebraic logic. Category theory: universal properties; constructions in categories; natural transformations and adjunctions; monads. Proof theory: lambda-calculus; intuitionistic logic and Curry-Howard correspondence; proof systems. Matrix theory: elementary divisors and invariant factors, minimal polynomial; canonical forms of a matrix; nonnegative matrix, irreducibility and primitivity.






António Machiavelo (UP), Luis Pinto (UM), Manuel Delgado (UP), Yulin Zhang (UM)

Advanced Topics in Analysis and Optimization (AO)

Vector spaces: normed linear spaces; Banach spaces; separability; Lp-spaces. Hahn-Banach Theorem: Open Mapping Theorem; dual spaces; reflexivity; weak and weak-* topologies. Hilbert spaces: the Projection Theorem; Stampacchia e Lax-Milgram Theorems; Riesz Representation Theorem. Application of the Hahn-Banach theorem to minimum norm problems. Optimization of functionals: Gateaux and Frechet derivatives; Euler-Lagrange equations; problems with constraints; convex-concave functionals; conjugate functionals; dual optimization problems. Global constrained optimization: Lagrange multipliers; sufficiency; sensitivity; duality. Local constrained optimization: Inverse function equality and inequality constraints. Application to optimal control: Pontryagin maximum principle.






Assis Azevedo (UM), Fernando Lobo Pereira (UP)

Advanced Topics in Dynamics and Geometry (DG)

Elementary geometry of submanifolds of R^n: Parametrisations (or charts), tangent bundle, differentiable functions, submanifolds, transversality. Differential forms, de Rham cohomology. Basic concepts of dynamics in R^n (or in submanifolds of R^n): Differential equations, stability of equilibria and of periodic solutions, hyperbolicity, stable and unstable manifolds, Poincaré map. Structural stability and bifurcations. The same concepts for the dynamics of recurrence relations.






Domennico Catalano (UA), Isabel Labouriau (UP)

Advanced Topics in Probability and Statistics (PE)

Measurable spaces. Sequences of events. Measurable functions. Measures. Random variables, probability measures, fundamental properties. Probability spaces, types of probability laws. Integration in probability spaces and expectation. Inequalities. Some probability distributions. Independence and conditioning. Characteristic functions. Modes of convergence of sequences of random variables. Laws of large numbers. Central limit theorems. Multivariate distributions, conditional laws. Conditional expectation. Statistical models. Decision theory: risk functions, decision rules, criteria. Exponential families. Sufficiency. Point estimation, comparison of estimators, asymptotic properties, methods of estimation with emphasis on likelihood based inference. Hypothesis tests and confidence sets.






Cecília Azevedo (UM), Isabel Pereira (UA), Margarida Brito (UP), M. Emilia Athayde (UM)

Optional Courses

Information about the syllabi can be found here here.

During the academic year 2016/2017, with the authorization of the scientific committee and in accordance with the preferences of students, the optional courses that will be taught will be chosen, making the most effective use of resources, from the following list of courses:








Research Project in Mathematics

It is intended that each student, with the help of his/her supervisor, study a recent topic/field of research in mathematics and its applications. This study leads to (i) the written Report (thesis proposal) and (ii) an oral presentation. The Report lays out the plan of the research, describing the state-of-the-art, the scientific foundations, the methodology to be used and the objectives that are expected to achieve.






Corália Vicente (UP), Delfim Torres (UA), Fernando Lobo Pereira (UP), Lisa Santos (UM), Sílvio Gama (UP), Sofia Castro (UP)


The students are expected to attend the regularly organised seminars given by the program's teaching staff and write a summary with discussion for part of these seminars.  Each student is also expected to choose one of the research themes proposed on these seminars and prepare a talk on that subject, under the advice and guidance of a supervisor of his/her choice.






Cláudia Mendes Araújo (UM), Lisa Santos (UM)

2nd Year



3rd Year



4th Year




Specialised seminars will be organised during the academic year.

An overview of the Deep Learning Method” , Stéphane Clain, October 11, 14h30 – 15h15, UM

Mathematical models for infectious diseases and optimal control”, Cristiana Silva, October 18, 14h30 – 15h15, UA

Longitudinal data analysis in biostatistics”, Inês Sousa, October 25, 14h30 – 15h15, UM

Models for time series of counts”,Eduarda Silva, November 8, 14h30 – 15h15, UP

Research challenges in stochastic frontier analysis with maximum entropy estimation“, Pedro Macedo, November 9 14h30 – 15h15, UA

Applicable generalized inverses of matrices“, Pedro Patrício, November 15, 14h00 – 14h45, UP

Learning from data streams“, João Gama, November 15, 15h00 – 15h45, UP

Abstract regular polytopes“, Elisa Fernandes, November 22, 14h30 – 15h15, UA

An ODE model of immune response by T cells“, Bruno Oliveira, November 29, 14h30 – 15h15, UP

Dynamic neural fields: theory and applications“, Wolfram Erlhagen, November 30, 14h30 – 15h15, UM

Mathematical problems of general relativity“, Filipe Mena, December 6, 14h30 – 15h15, UM

A graph of all numerical semigroups“, Manuel Delgado, December 9, 14h30 – 15h15, UP

Linear statistical models: an overview“, A. Manuela Gonçalves and Susana Faria, December 13, 14h00 – 14h45, UM

Representations of fundamental groups of surfaces“, Peter Gothen, December 13, 15h00 – 15h45, UP

Multi-vehicle identification and tracking of oceanic lagrangian coherent structures“, João Tasso, December 20 14h00 – 14h45, UP 

An optimal control framework for sustainable resources management in agriculture“, Fernando Lobo Pereira, December 20, 14h00 – 14h45, UP

Research themes in Logic and Computation“, José C. Espírito Santo, January 10, 14h00 – 14h45, UM

On co-algebraic dualities“, Dirk Hofmann, January 10, 15h00 – 15h45, UA