Filipe C. Mena

Full Professor (Professor Catedrático)
Vice-President of the Department of Mathematics, Instituto Superior Técnico, Univ. Lisboa, Portugal

(Last update: February 2024)

Research interests

General Relativity, Mathematical Physics, Differential Geometry:
Analysis and stability problems of the Einstein equations. Theory and applications of non-linear perturbations.
Spacetime singularities and black holes. Mathematical Cosmology.

Academic and Research Work

(2024----) Full Professor, Dep. Mathematics, Instituto Superior Técnico, Univ. Lisboa.
(2018-24) Associate Professor, Dep. Mathematics, Instituto Superior Técnico, Univ. Lisboa.
(2009-18) 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), LJLL, Sorbonne Univ., Paris (4 months, 2017).
(2016-17) Habilitation in Mathematics, Univ. Minho.
(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. in Mathematics, Queen Mary, University of London, U.K.
(1990-94) Licenciatura in Physics/Applied Mathematics (4 year degree), University of Porto.

Funded Research Projects

(2023---) Coordinator of the Horizon Europe Marie Curie (SE) Project EinsteinWaves: "Einstein gravity and nonlinear waves: physical models, numerical simulations and data analysis". Participant institutions: IST (Portugal), Sorbonne (Paris), Copenhagen (Denmark), Tubingen (Germany) and associates Kyoto (Japan), Cordoba (Argentina) and Perimeter (Canada).
(2017-21) Member of H2020 COST action GWverse: Gravitational waves, black holes and fundamental physics.
(2019-20) Member of H2020 COST action CANTATA: Cosmology and Astrophysics Network for Theoretical Advances and Training Actions.
(2016-19) 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 team 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 team 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 team 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

Spacetime asymptotic structure (Mariem Magdy, ongoing, Funded by CAMGSD, IST).

Dynamics of scalar field spacetimes in General Relativity (Rodrigo Fontana, 2018-19, Funded by UFS, Brasil).

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

Evolution and stability problems of the Einstein equations (Francisco Pais, ongoing, CAMGSD grant). Co-supervision by Rita Teixeira da Costa (Cambridge).

Beyond General Relativity: Black Holes and Gravitational Waves (M. Margarida Lima, ongoing, FCT grant). Co-supervision by Cláudio Gomes (Açores).

Dynamical Systems in General Relativity (Vitor Bessa, 2022, FCT grant PD/BD/142891/2018). Co-supervision by Artur Alho (IST, Lisbon).

Stability of spacetimes with ergo-regions (João Oliveira, 2020, FCT grant PD/BD/128184/2016). Co-supervision by Carlos Herdeiro (Aveiro).

Critical phenomena in gravitational collapse and black hole formation (Paulo Luz, 2019, FCT grant PD/BD/114074/2015). Co-supervision by José Sande Lemos (IST, Lisbon).

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

Evolution of symmetric initial data for the Einstein Equations (Francisco Pais, 2023). Co-supervision by Edgar Gasperin (IST, Lisbon).

Magnetic Field in theories of gravity with non-minimal coupling between curvature and matter (Margarida Lima, 2021). Co-supervision by Orfeu Bertolami (Porto).

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).

Mechanics of Rigid Bodies and Applications to Planetary Dynamics (Rui Faria, 2014). Co-supervision by Filipe Moura (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 Supervision

Geometry and Analysis of the Einstein equations (Pedro Ronda, 8 month grant from Gulbenkian Foundation - Novos Talentos da Matemática, 2022-23).

Brownian motion and relativistic diffusion (Nuno Camarneiro, 8 month grant from Gulbenkian Foundation - Novos Talentos da Matemática, 2021-22). Co-supervision by Patrícia Gonçalves (IST, Lisbon).

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

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