Filipe Carteado Mena

Associate Professor with Habilitation, Department of Mathematics and Applications, University of Minho, Braga, Portugal.

(Last update: October 2017)

Research interests

General Relativity, Mathematical Cosmology, Differential Geometry:
Stability and genericity problems in General Relativity. Theory and applications of non-linear perturbations.
Spacetime singularities and black holes. Global evolution of the Einstein Equations.

Applications of Dynamical Systems (to Finance, Life Sciences and Physics):
Modelling and forecasting of interest rates in Finance. Dynamical systems and optimal control theory in Epidemiology.

Academic and Research Work

(2017----) Associate Professor with Habilitation, Dep. Mathematics and Applications, Univ. Minho. Research Visitor at LJLL, Univ. Paris 6 (4 months, 2017).
(2016-17) Habilitation in Mathematics, Univ. Minho.
(2009-17) Associate Professor, Dep. Mathematics and Applications, Univ. Minho. Research visitor at CBPF, Rio de Janeiro (6 months, 2010), Dep. Physics, Yale University, U.S.A. (3 months, 2011), UERJ, Rio de Janeiro (6 months, 2013 and 2014).
(2002-09) Auxiliar Professor, Dep. Mathematics, Univ. Minho. Research visitor at HSBC bank, London, U.K. (3 months, 2009) and Dep. Mathematics, IST, Lisbon (6 months, 2008). Long term Research Visitor at Queen Mary, University of London, U.K.
(2003-05) Posdoctoral Researcher, Mathematical Institute, University of Oxford, U.K. Posdoctoral research grants from Fundação para a Ciência e Tecnologia (2004-05) and Fundação Calouste Gulbenkian (2003-04).
(1998-02) Ph.D., Queen Mary, University of London, U.K., Ph.D. grant from Fundação para a Ciência e Tecnologia.
(1995-02) Teaching Assistent, Dep. Mathematics, Univ. Minho
(1994-95) M.Sc., Queen Mary, University of London, U.K.
(1990-94) Licenciatura (4 year degree), University of Porto.

Administrative Positions

(2013----) Head of the Geometry, Topology and Mathematical Physics Research Group of the Centre of Mathematics
(2013-16) Member of the School Council of the School of Sciences
(2011-13) Vice-Director of the Ph.D. Programme in Mathematics and Applications of the Universities of Aveiro and Minho, also in (2008-09)
(2011-13) Member of the Pedagogical Council of the School of Sciences
(2009-10) Head of Department of Mathematics
(2008-09) Vice-Head of Dep. Mathematics
(2008-10) Head of the Mathematical Physics Research Group of the Centre of Mathematics
(2006-10) Member of the Directive Commitee of the Centre of Mathematics
(2003-04) Member of the Coordinating Commitee of the Dep. Mathematics

Funded Research Projects

(2016----) Local Coordinator at U. Minho of FCT project PTDC/MAT-ANA/1275/2014: "Global properties of solutions of the Einstein equations", participant institutions: CMAT (Minho), CAMGSD (IST) and UNIDE (ISCTE)
(2012-15) Member of project FCT/CERN/FP/123609/2011: "String effects in Black Holes and Particle Physics", based at CMAT (Minho).
(2010-12) Member of project FCT/CERN/FP/116377/2010: "Black Holes and String Theory", based at CMAT (Minho).
(2010-12) Coordinator of FCT Project PTDC/MAT/108921/2008: "Analysis of the Einstein Equations", participant institutions: CMAT (Minho) and CAMGSD (IST).
(2008-10) Coordinator of the portuguese part of Project B-29/08 of CRUP/British Council (U.K.), participant institutions: CMAT (Minho), CAMGSD (IST), Math. Inst. (Oxford, U.K.)
(2004-06) Coordinator of the portuguese part of Project E-113/04 of CRUP/Ministerio de Ciencia y Tecnologia (Spain), participant institutions: CMAT (Minho), Dep. Física (Salamanca, Spain), Dep. Física (Bilbao, Spain)
(2003-05) Coordinator of the portuguese part of Project B-13/03 of CRUP/British Council (U.K.), participant institutions: CMAT (Minho), School Math. Sci. (Queen Mary, London, U.K.), Inst. Cosmology (Porstmouth, U.K.)

Posdoc Supervision

  • Quasi-local holography, higher dimensional black hole systems and non-extensive black hole thermodynamics (Viktor Czinner, 2012-2015, Marie Curie Fellow DFRH/WIIA/28/2011, FCT Welcome II Programme).
  • Higher dimensional black hole systems and non-extensive black hole thermodynamics (Jacobo Diaz-Polo, 2013-14, Marie Curie/FCT Research grant (BI) within project DFRH/WIIA/28/2011). Co-supervision by Viktor Czinner (Minho).
  • Black hole in generic space-times, gravitational radiation and phenomenology: numerical and analytical methods (Carmen Rebelo, 2012-2014, FCT grant SFRH/BDP/77223/2011). Co-supervision by Carlos Herdeiro (Aveiro).

    • Ph.D. Supervision

  • Dynamical Systems in General Relativity and in Modified Gravity Theories (Vitor Bessa, ongoing, FCT grant). Co-supervision by Artur Alho (IST, Lisbon).
  • Stability of spacetimes with ergo-regions (João Oliveira, ongoing, FCT grant PD/BD/128184/2016). Co-supervision by Carlos Herdeiro (Aveiro).
  • Critical phenomena in gravitational collapse and black hole formation (Paulo Luz, ongoing, FCT grant PD/BD/114074/2015). Co-supervision by José Sande Lemos (IST, Lisbon).
  • Applications of Dynamical Systems in Economics and Actuarial Sciences (Isabel Duarte, ongoing, FCT grant SFRH/BD/33502/2008). Co-supervision by Alberto Pinto (Porto).
  • Non-linear evolution and stability problems in General Relativity (Artur Alho, 2012, FCT grant SFRH/BD/48658/2008). Co-supervision by José Natário (IST, Lisbon).

    • M.Sc. Supervision

  • Mechanics of Rigid Bodies and Applications to Planetary Dynamics (Rui Faria, ongoing). Co-supervision by Filipe Moura (Minho).
  • Gravitational colapse and black hole formation (João Oliveira, 2016).
  • Applications of Statistical Methods to Economics and Finance (Marílio Meireles, 2016). Co-supervision by Raquel Menezes (Minho).
  • Non-linear First Order Partial Differential Equations (Alexandra Gaspar, 2013). Co-supervision by Mahendra Panthee (Minho).
  • Forecasting and Analysis of Interest Rates in Finance (Cristiana Vieira, 2012). Co-supervision by Raquel Menezes (Minho).
  • Qualitative Theory of Differential Equations and Applications to Biology (António Correia, 2009). Co-supervision by Ana J. Soares (Minho).
  • Semi-relativitic approximation of the restricted three body problem (Ana Fernandes, 2007)
  • Stability of the restricted three body problem (Dulce Pinto, 2006) online (in portuguese)

    • Research Initiation Grant (BI) Supervision

  • Global properties of solutions to Einstein's equations (Vitor Bessa, 4 month BI grant from project PTDC/MAT-ANA/1275/2014, 2017). Co-supervision by Artur Alho (IST, Lisbon).
  • Metric junctions and black hole formation in General Relativity (Margarida Lima, 3 month BI grant from CMAT, Univ. Minho, 2016).

    • Undergraduate Supervision

  • Differential Geometry and General Relativity (Margarida Lima, 2017). Co-supervision by Irene Brito (Minho).
  • Schwarzschild solution and tests to General Relativity (Armindo Figueira, 2009). Co-supervision by Filipe Moura (Minho).
  • Games in Mathematics Teaching (Cristina Carvalho, Orquídea Pereira, Sabrina Rodrigues, 2008)
  • Mathematics in Astronomy (Fátima Gonçalves, Liliana Magalhães e Susana Pereira, 2007) pdf (in portuguese)
  • Hamiltonian Graphs (Álvara Costa, 2006) pdf (in portuguese)

    Teaching (Undergraduate and M.Sc. levels)

    At the University of Minho, courses about to Calculus, Analysis, Differential Equations, Linear Algebra and Analytic Geometry, Differential Geometry, Dynamical Systems, Mathematical Modelling and Mathematical Methods of Physics. At the Universities of London and Oxford, courses about General Relativity.

    List of Publications

    The complete list is here. A sample with different topics is:

  • Marc Mars (Salamanca), Filipe C. Mena and Raul Vera (Bilbao)
    Review on exact and perturbative deformations of the Einstein-Straus model: uniqueness and rigidity results
    (in Topical Collection: Progress in Mathematical Relativity with Applications to Astrophysics and Cosmology)
    General Relativity and Gravitation, vol. 45 (2013) 2143-2173 online

  • Irene Brito (Minho), Jaume Carot (Palma Maiorca), Filipe C. Mena and Estelita L. R. Vaz (Minho)
    Cylindrically symmetric static solutions of the Einstein Field Equations for elastic matter
    Journal of Mathematical Physics, vol. 53 (2012) 122504 (16 pages)

  • Artur Alho (Minho) and Filipe C. Mena,
    Pre-inflationary homogeneization of scalar field cosmologies
    Physics Letters B, vol. 703 (2011) 537-542

  • Filipe C. Mena, Jose Natario (Lisbon) and Paul Tod (Oxford)
    Formation of Higher-dimensional Topological Black Holes
    Annales Henri Poincaré, vol. 10 (2010) 1359-1376 online

    • Address, Phone and Fax

    Departamento de Matemática e Aplicações, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal.
    Office: EC.3.19, Tel: +351 253 604087 (direct), Fax: +351 253 604369 (dept.)
    Email: fmena(at)math(dot)uminho(dot)pt