Cookie usage policy

The website of the University Carlos III of Madrid use its own cookies and third-party cookies to improve our services by analyzing their browsing habits. By continuing navigation, we understand that it accepts our cookie policy. "Usage rules"

Mathematical Engineering

  • Inicio



    Prof. David Delgado Gómez



    About the program


    The Ph.D. Program in Mathematical Engineering is the natural continuation of the studies leading to a Master’s Degree in Mathematical Engineering

    The program may include advanced training for the elaboration and presentation of an original research project as content of the Ph.D. thesis, in accordance with the lines of research established by the six departments participating in the program.



    The program provides students with the required tools to deal with technological or scientific problems by means of

    • A precise mathematical / physical / statistical foundation
    • A formulation of a model in mathematical terms
    • A theoretical and/or numerical solution of a model
    • The analytical skills to solve complex problems in engineering


    • Program regulated by RD 99/2011, January 2018







    Student profile


    These skills require the use of mathematical tools that help physical phenomenon modeling and statistical tools to enable the formulation of empirical models from observation. Some experience is also required in managing mathematical computer programs (like, Mathematica, MatLab, or R).

    The languages used in the training process will be Spanish and/or English, so it is necessary to have a good knowledge of these languages.


    Admission requirements


    The program’s admission requires a Bachelor's degree or equivalent and Master’s Degree, (at least 60 ECTS credits), with quantitative training in the area of Mathematical Engineering.

    The same requirements apply to applicants with equivalent studies in foreign educational systems. No homologation of degrees is required, if sufficient proof is given of a background comparable to a Spanish Bachelor and Master’s degrees and allows access to Ph.D. studies in the issuing country.

    Students with quantitative training in the area of Mathematical Engineering will be considered for direct admission to the Ph.D.

    Students trained in other areas may be admitted with the requirement of an additional specific training up to 30 ECTS credits.

    Finally, applicants with other Spanish Ph.D.’s may be admitted.

    Admission criteria


    Admission is determined according to the criteria set by the Academic Committee listed below. These are implemented by the coordinator of the program, who reports to the Committee on a regular basis. 

    Admission is based on merit and capacity of the candidates, for which the following aspects are considered:

    • Academic record of previous studies
    • Curriculum Vitae
    • Endorsement letters from professors of the university or from other institutions or organizations, with direct knowledge of the capacity and competence of the candidate
    • Thesis project proposal, provided by the candidate
    • Connection of the project with the lines of research of the Ph.D. Program. The thesis project can be endorsed by a professor from the program
    • A personal interview can be conducted if deemed necessary, with at least one member of the Academic Committee being present

    Besides the thesis project proposal, the updated CV and the copies of academic certificates must also be provided by the candidate.

    Endorsement letters must be submitted by the professors to (indicating full name of the candidate-Ph.D. in Mathematical Engineering-uc3m).

    The Academic Committee will determine the convenience of a personal interview and the weight of each criteria listed above: academic background and training of the candidate (minimum 50%); interest and suitability of the project for the lines of research of the program (minimum 30%).

    The admission criteria and procedures are equal for part-time and full-time candidates.

    Resolutions of admission to the program may require up to 30 ECTS credits of complementary training. The Academic Committee will determine the specific subjects and research work of the complementary training, with input from the tutor and thesis advisor. Full-time students will take these credits during the first year on the program. Part-time students will take these credits during their first two years.



    Seats available for the academic year: 17




    In addition to the elaboration of the doctoral thesis, students must take some training aimed at improving their research skills and the scientific quality of their research work. This is structured in the following types of training.


    Specific training 


    • Seminars and specialized courses by visiting experts on the latest advanced techniques in the different areas of specialization.


    Research skills training

    Optional training. Up to 6 credits during the doctoral training period.

    Research skills training is focused on abilities common to all disciplines for the development of scientific and educational skills and the improvement of the professional career. This training consists of different activities (short courses, seminars, etc.), which can be recommended by the Academic Committee of the program.


    Further information:

    • Lines of research

      Applied Mathematics for control, systems and signals

      Complex systems

      Partial differential equations

      Numerical analysis of partial differential equations​

      Evolution and theoretical ecology, dynamics of socioeconomic systems and game theory

      Statistical mechanics and nonlinear dynamics, materials science and nanostructures, microfluidics and fluid absorption of structured substrates

      Social networks

      Numerical Linear Algebra​

      Applied Harmonic Analysis,  Applied functional analysis​

      Mathematics for quantum mechanics, Quantum information​

      Non-linear load and spin transport in nano-structures. NEMS systems: nano-electro-mechanical. Two-dimensional materials. Active matter. Vasculature growth. Biological systems​

      Dynamic multivariate modeling in business and industry​

      Parametric and non-parametric statistics for complex data​

      Decision-making problems and data analysis in high dimension​

      Statistical methods of decision through data analysis (not high dimension)

      Approximation Theory

      Geometric Function Theory​

      Graph Theory​

      Biomedical image processing and image formation, Modeling and numerical simulation, Inverse problems


      Markovian decision models

      Mathematical physics: field theory and statistical physics​


    • Scientific results

      This is a sample of relevant publications derived from doctoral thesis work over the last five years:

      • Thesis: Modelos de oscilaciones caóticas en superredes semiconductoras a temperatura ambiente
        Author: Emanuel Gastón Mompó Pavesi
        Publication: Coherence Resonance and Stochastic Resonance in an Excitable Semiconductor Superlattice. E. M. Mompo, M. Ruiz-Garcia, M. Carretero, H. T. Grahn, Y. H. Zhang, y L. L. Bonilla
        Journal: Physical Review Letters, 121, 086805 (2018) (6 pp).
        Area: Physics Multidisciplinary
        Ranking position in area in 2018: 6/81 (Q1)
        Impact factor: 9.227, Google Scholar citations: 8. WOS citations: 4
      • Thesis: Modeling and simulation of bacterial biofilm growth
        Author: Sergei Iakunin
        Publication: Variational formulation, asymptotic analysis, and finite element simulation of wrinkling phenomena in modified plate equations modeling biofilms growing on agar substrates. S. Iakunin y L. L. Bonilla
        Journal: Computer Methods in Applied Mechanics and Engineering. 333, 257-286 (2018).
        Area: Mathematics Interdisciplinary Applications
        Position in area in 2018: 2/105 (Q1)
        Impact factor: 4.821. Google Scholar citations: 4. WOS citations: 2
      • Thesis: Models in molecular evolution: the case of toyLIFE
        Author: Pablo Catalán Fernández
        Publication: Adding levels of complexity enhances robustness and evolvability in a multilevel genotype–phenotype map. Catalán, P., Wagner, A., Manrubia, S. and Cuesta, J. A.
        Journal: Journal of the Royal Society Interface 15:20170516 (2018)
        Area: Multidisciplinary Sciences
        Ranking position in area in 2016: 12/64 (Q1)
        Impact factor: 3.579
      • Thesis: Nonlinear effects in low-dimensional systems: graphene membrane and electron transport in semiconductor superlattices
        Author: Miguel Ruiz García
        Publication: Bifurcation analysis and phase diagram of a spin-string model with buckled states. M. Ruiz-Garcia, L. L. Bonilla y A. Prados
        Journal: Physical Review E, 96, 062147 (2017) (14 pp).
        Area: Physics Mathematical
        Ranking position in area in 2017: 7/55 (Q1)
        Impact factor: 2.284, Google Scholar citations: 5. WOS citations: 2
      • Thesis: Modelo y simulación del transporte electrónico en superredes semiconductoras en un campo magnético externo
        Author: Andrés Segura Aragonés
        Publication: Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice. L. L. Bonilla, M. Carretero y A. Segura
        Journal: Physical Review E, 96, 062215 (2017) (10 pp).
        Area: Physics Mathematical
        Ranking position in area in 2017: 7/55 (Q1)
        Impact factor: 2.284, Google Scholar citations: 2. WOS citations: 2
      • Thesis: Classical perturbations for matrices of linear functionals
        Author: Juan Carlos García Ardila
        Publication: Christoffel transformations for matrix orthogonal polynomials in the real line and the non-Abelian 2D Toda lattice hierarchy. C. Alvarez Fernández, G. Ariznabarreta, J. C. García Ardila, F. Marcellán, M. Mañas
      • Thesis: High Order Numerical Methods for Myxobacteria Pattern Formation
        Author:  Ana Maria Glavan
        Publication: Wavelength selection of rippling patterns in myxobacteria. L. L. Bonilla, A. Glavan y A. Marquina
        Journal: Physical Review E, 93, 012412 (2016) (13 pp).
        Area: Physics Mathematical
        Ranking position in area in 2016:  6/55 (Q1)
        Impact factor: 2.366, Google Scholar citations: 3. WOS citations: 3
      • Thesis: Gráficos de control EWMA adaptativos con parámetro de suavizado variable en el tiempo
        Author: Willy Ericson Ugaz Sánchez
        Publication: Adaptive EWMA control charts with time-varying smoothing parameter. Willy Ugaz, Ismael Sánchez, Andrés M Alonso
        Journal: The International Journal of Advanced Manufacturing Technology, 93 (2017)
        Ranking position in area in 2017: Q2
      • Thesis: Alliance polynomial and hyperbolicity in regular graphs
        Author: Yadira Torres Núñez
        Publication: Alliance polynomial of regular graphs. W. Carballosa, J. M. Rodríguez, J. M. Sigarreta, Y. Torres-Nuñez
        Journal: Discrete Applied Mathematics 225, 22-32 (2017)
        Area: Mathematics Applied
        Ranking position in area in 2016: 118/255 (Q2)
        Impact factor: 0.956
      • Thesis: Matrices de Fiedler: propiedades numéricas y estructurales
        Author: Javier Pérez Álvaro
        Publication: Backward stability of polynomial root-finding using Fiedler companion matrices. F. De Terán, F. M. Dopico y J. Pérez
        Journal: IMA Journal of Numerical Analysis, 36, pp. 133-173 (2016)
        Area: Mathematics Applied
        Ranking position in area in 2016: 38/255 (Q1)
        Impact factor: Google Scholar citations: 19. WOS citations: 5
      • Thesis: Structured condition numbers for parameterized quasiseparable matrices
        Author: Kenet Jorge Pomés Portal
        Publication: Structured eigenvalue condition numbers for parameterized quasiseparable matrices. F. M. Dopico y K. Pomés
        Journal: Numerische Mathematik, 134, pp. 473–512 (2016)
        Area: Mathematics Applied
        Ranking position in area in 2016: 21/255 (Q1)
        Impact factor: Google Scholar citations: 3. WOS citations: 3
      • Thesis: Small values of the hyperbolicity constant in graphs
        Author: Omar Rosario Cayetano
        Publication: Small values of the hyperbolicity constant in graphs. S. Bermudo, J. M. Rodríguez, O. Rosario, J. M. Sigarreta
        Journal: Discrete Mathematics 339, 3073-3084 (2016)
        Area: Mathematics
        Impact factor in 2016: 0.698
      • Thesis: Mobility and interaction patterns in social networks
        Author: Alejandro Llorente Pino
        Publication: Social media fingerprints of unemployment. Llorente, A., Garcia-Herranz, M., Cebrian, M., & Moro, E. (2015)
        Journal: PloS one, 10(5), e0128692
        Area: Multidisciplinary
        Ranking position in area in 2015: Q1
        Impact factor: 65 citations
      • Thesis: Fourier series and orthogonal polynomials in Sobolev spaces
        Author: María Francisca Pérez Valero
        Publication: Asymptotic behavior of the partial derivatives of Laguerre kernels and some applications. F. Marcellan, M. F. Perez Valero, Y. Quintana
        Journal: Journal Mathematical Analysis and Applications 421, 314-328 (2015)
        Ranking position in area in 2015: Q1
      • Thesis: Multiphysics modeling of liquid-feed direct methanol fuel cells and characterization of diffusive transport properties of gas diffusion layers
        Author: Pablo Ángel García Salaberri
        Publication: García-Salaberri, P. A., Hwang, G., Vera, M., Weber, A. Z., & Gostick, J. T. Effective diffusivity in partially-saturated carbon-fiber gas diffusion layers: Effect of through-plane saturation distribution
        Journal: International Journal of Heat and Mass Transfer, 86, 319-333 (2015)
        Ranking position in area in 2015: Q1
        Impact factor: Scholar citations: 50. Scopus citations: 42
      • Thesis: The Multivariate Directional Approach: High Level Quantile Estimation and Applications to Finance and Environmental Phenomena
        Author: Raúl Andrés Torres Díaz
        Publication: A directional multivariate Value at Risk. Torres R., Lillo R.E., and Laniado H.
        Journal: Insurance: Mathematics and Economics, 65, 111-123 (2015)
        Area: Statistics and Probability
        Ranking position in area in 2015: Q2
        Impact factor: 11 citations
      • Thesis: Evolutionary Games in Networked Populations: Models and Experiments
        Author: Alberto Antonioni
        Publication: Short-range mobility and the evolution of cooperation: an experimental study. Alberto Antonioni, Marco Tomassini and Angel Sánchez
        Journal: Scientific Reports 5, 10282 (2014)
        Area: Multidisciplinary Sciences
        Ranking position in area in 2014: 5/55 (Q1)
        Impact factor: 5.578. 5 citations
      • Thesis: Gromov Hyperbolicity of Several Products of Graphs
        Author: Amauris de la Cruz Rodríguez
        Publication: Gromov hyperbolicity in strong product graphs. W. Carballosa, R. M. Casablanca, A. de la Cruz, J. M. Rodríguez
        Journal: Electronic Journal of Combinatorics 20(3), p.2 (2013)
        Area: Mathematics
        Ranking position in area in 2013: 156/299 (Q2)
        Impact factor: 0.568
      • Thesis: Achieving reliability and fairness in online task computing environments
        Author: Evgenia Christoforou
        Publication: Applying the dynamics of evolution to achieve reliability in master-worker computing. Evgenia Christoforou, Antonio Fernández Anta, Chryssis Georgiou, Miguel A. Mosteiro, and Angel Sánchez
        Journal: Concurrency and Computation: Practice and Experience 25, 2363-2380 (2013)
        Area: Computer Science, Theory and Methods
        Ranking position in area in 2013: 50/102 (Q2)
        Impact factor: 0.784, 13 citations
      • Thesis: Analytic properties of polynomials ortHogonal with respect to coherent pair of measures supported on the unit circle
        Author: Lino Gustavo Garza Gaona
        Publication: A matrix approach for the semiclassical and coherent orthogonal polynomials. L. G. Garza, L. E. Garza, F. Marcellán, N. C. Pinzón-Cortés
        Journal: Applied Mathematics and Computation
        Ranking position in area: Q1
    • Scientific publications

      This is a sample of relevant faculty publications:

      Department of Statistics

      • Grané, Aurea, and Romera, R. “On visualizing mixed-type data: A joint metric approach to profile construction and outlier detection”. Sociological Methods and Research, vol. 47 (2), 207-239 (2018)
      • Torabi, H., Montazeri, N.H. and Grané, Aurea. “A wide review on exponentiality tests and two competitive proposals with application on reliability”. Journal of Statistical Computation and Simulation, vol. 88 (1), 108-139 (2018)
      • Velilla, Santiago. “A note on collinearity diagnostics and centering”. The American Statistician. In press (published online in 2018)
      • Velilla, Santiago, Nguyen, H. “A Goodness-of-Fit test for VARMA(p,q) models”. Journal of Statistical Planning and Inference (published online in 2018)
      • Alonso, Andrés, D’Urso, P. and Maharaj, E.A. "Fuzzy Clustering of Time Series using Extremes. Fuzzy Sets and Systems, 318, 56–79 (2017)
      • Sarhadi, A., Ausín, María Concepción and Wiper, M.P. “A New Time-varying Concept of Risk in a Changing Climate”. Nature Scientific Reports (2017). Forthcoming.
      • Gómez, M. Ausín, María Concepción and Domínguez, M.C. “Seasonal copula models for the analysis of glacier discharge at King George Island, Antarctica”. Stochastic Environmental Research and Risk Assessment, 31, 1107-1121 (2017)
      • Galeano, Pedro and Wied, D. “Dating multiple change points in the correlation matrix”.  Test, 26, 331-352 (2017)
      • Febrero-Bande, M., Galeano, Pedro and González-Manteiga, W. “Functional Principal Component Regression and Functional Partial Least-squares Regression: An Overview and a Comparative Study”. International Statistical Review, 85, 61-83 (2017)
      • Nogales, Francisco Javier, Avagyan, A. and Alonso, A. “D-trace Precision Matrix Estimation Using Adaptive Lasso Penalties'' Advances in Data Analysis and Classification (2017)
      • Nogales, Francisco Javier, Avagyan, V. and Alonso, A. “Improving the Graphical Lasso Estimation for the Precision Matrix Through Roots of the Sample Covariance Matrix”. Journal of Computational and Graphical Statistics (2017)
      • Alonso, Andrés, Bastos, G. and García-Martos, C. “Electricity Price Forecasting by Averaging Dynamic Factor Models". Energies, 9, 1-21 (2016)
      • Pino, J., Tena, J. and Espasa, Antoni. “Geographical disaggregation of sectoral inflation. Econometric modelling of the Euro Area and Spanish economies”. Applied Economics, v.48, Issue 9, pp. 799-815 (2016)
      • Lillo, Rosa, Galeano, P. and Joseph, E. “The Mahalanobis distance for functional data with applications to classification”. Technometrics (2016)
      • Niño-Mora, José. “Whittle's index policy for multi-target tracking with jamming and nondetections”. En Proceedings of ASMTA 2016, the 23rd International Conference on Analytical & Stochastic Modelling Techniques & Applications, Lecture Notes in Computer Science, vol. 9845, pp. 210–222, Springer (2016)
      • Peña, Daniel and Yohai, V. “Generalized Dynamic Principal Components” The Journal of American Statistical Association (2016) (in press)
      • Peña, Daniel, Nieto, F. H. and Saboyá, D. “Common Seasonality in Multivariate Time Series”. Statistica Sinica (2016) (in press)
      • Romera, Rosario, and Grané, A. “On visualizing mixed-type data: A joint metric approach to profile construction and outlier detection”. Sociological Methods and Research (2016)
      • Romo, Juan, Martín Barragán, B. and Lillo, R. "Functional boxplots based on epigraphs and hypographs" Journal of Applied Statistics, 43(6), 1088-1103 (2016)
      • Wiper, Michael, Sarhadi, A., Burn, D.H. and Ausín, M.C. “Time Varying Non-stationary Multivariate Risk Analysis Using a Dynamic Bayesian Copula". Water Resources Research, 52, 2327-2349 (2016)
      • Veiga, Helena, Galán, J. and Wiper, M. “Dynamic Effects in Inefficiency: Evidence from the Colombian Banking Sector”. European Journal of Operational Research, 20(2), 562-575 (2015)
      • Wiper, Michael, G.Nuñez, A. and Ausín, M.C. “Bayesian nonparametric models of circular variables based on Dirichlet process mixtures of normal distributions". Journal of Agricultural, Biological and Environmental Statistics, 20, 47-64 (2015)
      • Lillo, Rosa and Laniado, H. “Allocation policies of redundancies in two-parallel-series and two-series-parallel systems”. Transactions on Reliability, 63 (1), 223-229 (2014)
      • Molina, Isabel, Nandram, B. and Rao, J.N.K. (2014). Small Area Estimation of General Parameters with Application to Poverty Indicators: A Hierarchical Bayes Approach. Annals of Applied Statistics (2014)
      • Niño-Mora, José. “A dynamic page-refresh index policy for web crawlers”. En Proceedings of ASMTA 2014, the 21st International Conference on Analytical & Stochastic Modelling Techniques & Applications, Lecture Notes in Computer Science, vol. 8499, pp. 40–60, Springer (2014)
      • Veerman, J.J.P. and Prieto, Francisco J. “On Rank Driven Dynamical Systems” Journal of Statistical Physics, Vol. 156 (3), pp. 455–472 (2014)
      • Romo, Juan and Arribas, A. "Shape outlier detection and visualization for functional data: the outliergram”. Biostatistics, 15(4), 603-619 (2014)
      • Veiga, Helena and Grané, A. “Outliers, GARCH-type models and risk measures: A comparison of several approaches”. Journal of Empirical Finance, 26, 26-40 (2014)
      • Espasa, A. and Durban, María. “Discussion on: Short-Term Forecasting the Daily Load Curve for Residential”. Applied Stochastic Models in Business and Industry (2013)
      • Lee, D-J., Durban, María, Eilers, P. “Efficient two-dimensional smoothing with P-spline ANOVA mixed models and nested basis”. Computational Staistics & Data Analysis (2013)
      • Espasa, Antoni and Mayo-Burgos, I. “Forecasting Aggregate and Disaggregates with Common Features”. International Journal of Forecasting, v.29, n.4, pp.718-732 (2013)
      • Marhuenda, Y., Molina, Isabel and Morales, D. “Small area estimation with spatio-temporal Fay-Herriot models”. Computational Statistics and Data Analysis 58, 308-325 (2013)
      • Marín, Juan Miguel and Rodríguez-Bernal, M. T. "Multiple hypothesis testing and clustering with mixtures of non-central t-distributions applied in microarray data analysis". Computational Statistics and Data Analysis (2012)
      • Romera, Rosario, and Cañada, H. “Controlled diffusion processes with Markovian switchings for modeling dynamical engineering systems”. European Journal of Operational Research, 221 (3), 614-624 (2012)
      • Lobo, M.G., and Sánchez, Ismael. "Regional wind power forecasting based on smoothing techniques, with application to the Spanish peninsular system". IEEE Transactions on Power Systems, 27, 1990-1997 (2012)
      • Jiménez, Raúl. “Forensic analysis of the Venezuelan recall referendum”. Statistical Science (2011)
      • Jiménez, Raúl and Yukich, J. “Nonparametric estimation of surface integrals”. Ann. Statist.39, 232-260 (2011)
      • Albarran, I., Alonso, P.J. and Marin, Juan Miguel. "Non-linear models of disability and age applied to Census Data". J. of Applied Statistics (2011)
      • Avelino, C.P., Moguerza, J.M., Olivares, A. and Prieto, Francisco J. “Combining and scaling descent and negative curvature directions.” Mathematical Programming, Vol. 128, pp. 285–319 (2011)
      • Bermejo, M.A., Peña, D. and Sánchez, Ismael. "Identification of TAR models using recursive estimation". Journal of Forecasting, 30, 31-50 (2011)


      Department of Mathematics

      Research group 1

      • Córdoba-Torres, P., Santalla, S. N., Cuerno, Rodolfo and Rodríguez-Laguna, J. “Kardar-Parisi-Zhang Universality in First-Passage Percolation: the Role of Geodesic Degeneracy”. Journal of Statistical Mechanics: Theory & Experiment, 063212 (2018)
      • Redondo-Cubero, K., Lorenz, F. J., Palomares, A., Muñoz, M., Castro, J., Muñoz-García, Cuerno, Rodolfo and Vázquez, L. “Concurrent segregation and erosion effects in medium-energy iron-beam patterning of silicon surfaces”. Journal of Physics: Condensed Matter 30, 274001 (2018)
      • Dopico, Froilán Martínez, Lawrence, P.W., Pérez, J. and Dooren, P.Van “Block Kronecker linearizations of matrix polynomials and their backward errors”. Numer. Math. 140, no. 2, 373–426 (2018)
      • Bueno, M. I., Dopico, Froilán Martínez, Pérez, J., Saavedra, R. and Zykoski, B. “A simplified approach to Fiedler-like pencils via block minimal bases pencils”. Linear Algebra Appl. 547, 45–104 (2018)
      • García García, Antonio and Muñoz-Bouzo, M.J. “Sampling formulas involving differences in shift-invariant subspaces: a unified approach”. Numer. Funct. Anal. Optim., 39(6):677-688 (2018)
      • Delgado-Téllez, M., Ibort, Luis Alberto and Rodríguez de la Peña, T. “Solving quantum optimal control problems using Clebsch variables and Lin constraints”. J. Phys. A 51, no. 3, 035302, 16 pp (2018)
      • Ara, P., Li, K., Lledó, Fernando and Wu, J. “Amenability of coarse spaces and K-algebras”. Bulletin of Mathematical Sciences 8, 257-306 (2018)
      • Fabila-Carrasco, J.S., Lledó, Fernando and Post, O. “Spectral gaps and discrete magnetic Laplacians”. Linear Algebra and its Applications 547, 183-216 (2018)
      • Marcellán, Francisco, Quintana, Y., Rodríguez, José M. “Weighted Sobolev spaces: Markov-type inequalities and duality”. Bull. Math. Sci. 8, no. 2, 233–256 (2018)
      • Dueñas Ruiz, H., Marcellán, Francisco and Molano Molano, Alejandro. “Asymptotics of Sobolev orthogonal polynomials for Hermite (1,1)-coherent pairs”. J. Math. Anal. Appl. 467, no. 1, 601–621 (2018)
      • Gurin, P., Varga, S., Martínez-Ratón, Yuri and Velasco, E. “Positional ordering of hard adsorbate particles in tubular nanopores” Phys. Rev. E. 97, 052606 (2018)
      • Ferreira, R. and de Pablo, Arturo. “Grow-up for a quasilinear heat equation with a localized reaction in higher dimensions”. Rev. Mat. Complut. 31, no. 3, 805–832 (2018)
      • de Pablo, Arturo, Quirós, F. and Rodríguez, A. “Regularity theory for singular nonlocal diffusion equations”. Calc. Var. Partial Differential Equations 57, no. 5, 57:136 (2018)
      • Martínez-Pérez and Rodríguez, J.M. “New lower bounds for the Geometric-Arithmetic index”. MATCH Communications in Mathematical and in Computer Chemistry 79, 451-466 (2018)
      • Tamarit, I., Cuesta, J.A., Robin I., Dunbar, M. and Sánchez, Ángel. “Cognitive resource allocation determines the organization of personal networks”. Proceedings of the National Academy of Sciences of the USA 115 (33) 8316-8321 (2018)
      • De Terán, Fernando. “A geometric description of the sets of palindromic and alternating matrix pencils with bounded rank”. SIAM J. Matrix Anal. Appl. 39, 1116–1134 (2018)
      • De Terán, Fernando, Iannazzo, B., Poloni, F. and Robol, L. “Solvability and uniqueness criteria for generalized Sylvester-type equations”. Linear Algebra Appl. 542, 501–521 (2018)
      • Álvarez-Caudevilla, P., Colorado, Eduardo and Fabelo, R. “A higher order system of some coupled nonlinear Schrödinger and Korteweg-de Vries equations”. J. Math. Phys., 58, no. 11, 111503, 13 pp (2017)
      • Cuesta, José Antonio and Manrubia, S. “Enumerating secondary structures and structural moieties for circular RNAs”. Journal of Theoretical Biology 419, 375-382 (2017)
      • Iranzo, J., Cuesta, José Antonio, Manrubia, S., Katsnelson, M.I. and Koonin, E.V. “Disentangling the effects of selection and loss bias on gene dynamics”. Proceedings of the National Academy of Sciences (USA) 114, E5616-E5624 (2017)
      • García García, Antonio, Hernández-Medina, M.A. and Pérez-Villalón, G. “Sampling in unitary invariant subspaces associated to LCA groups”. Result. Math., 72:1725-1745 (2017)
      • Ciaglia, F. M., Di Cosmo, F., Ibort, Luis Alberto and Marmo, G. “Dynamical aspects in the quantizer-dequantizer formalism”. Ann. Physics 385, 769–781 (2017)
      • Gurin, P., Varga, S., González-Pinto, M., Martínez-Ratón, Yuri and Velasco, E. “Ordering of hard rectangles in strong confinement”. J. Chem. Phys. 146, 134503 (2017)
      • López-Gómez, J., Molina-Meyer, Marcela and Rabinowitz, Paul H. “Global bifurcation diagrams of one node solutions in a class of degenerate boundary value problems”. Discrete Contin. Dyn. Syst. Ser. B 22, no. 3, 923–946 (2017)
      • Ibort, A.; López Yela, A. and Moro, Julio. “A new algorithm for computing branching rules and Clebsch-Gordan coefficients of unitary representations of compact groups”. J. Math. Phys. 58, no. 10, 101702, 21 pp (2017)
      • Moscoso, Miguel, Novikovz, A., Papanicolaoux, G. and Tsogka, C. “Multifrequency Interferometric Imaging with Intensity-Only Measurements”. SIAM Journal on Imaging Sciences, Vol. 10, No. 3, pp. 1005-1032 (2017)
      • Granados, A., Pestana, Domingo, Portilla, A. and Rodríguez, J.M. “Gromov hyperbolicity in Mycielskian graphs”. Symmetry 9, no. 8, Paper No. 131, 20 pp. (2017)
      • Arvesú Carballo, Jorge and Durán, A. “Casorati type determinants of some q-classical orthogonal polynomials”. Proceedings of the AMS, 144 (4), pp. 1655-1668 (2016)
      • Kindelan, Manuel, Moscoso, M. and González-Rodríguez, P. “Finite Difference Formulas for Accurate High Frequency Components”. Mathematical Problems in Engineering, Vol.2016, Article ID 7860618, doi:10.1155/2016/7860618 (2016)
      • Kindelan, Manuel, Moscoso M. and González-Rodríguez, P. “Radial basis function interpolation in the limit of increasingly flat basis functions”. J. Comput. Phys. 307, 225-242 (2016)
      • Castro-González, N., Dopico, F.M. and Molera, Juan Manuel. “Multiplicative perturbation theory of the Moore-Penrose inverse and the least squares problem”. Linear Algebra Appl. 503, 1–25 (2016)
      • Kryvasheyeu, Y., Chen H., Obradovich, N., Moro, Esteban, Van Hentenryck, P., Fowler, J. and Cebrian, M. “Rapid assessment of disaster damage using social media activity”. Science Advances 2, e1500779 (2016)
      • Sosa, F. and Moro, Julio. “First order asymptotic expansions for eigenvalues of multiplicatively perturbed matrices”. SIAM J. Matrix Anal. Appl. 37, no. 4, 1478–1504 (2016)
      • Kindelan, M., Moscoso, Miguel and Gonzalez-Rodriguez, P. “Optimized Finite Difference Formulas for Accurate High Frequency Components”. Mathematical Problems in Engineering, Vol.2016, Article ID 7860618, 15 pages (2016)
      • Hernández, V., Pestana, Domingo and Rodríguez, J.M. “Bounds on Gromov hyperbolicity constant”. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 110, no. 2, 321–342 (2016)
      • Rodríguez, J. M. and Sigarreta, J.M. “Spectral properties of geometric-arithmetic index”. Applied Mathematics and Computation 277, 142-153 (2016)
      • Poncela-Casasnovas, J., Gutiérrez-Roig, M., Gracia-Lázaro, C., Vicens, J., Gómez-Gardeñes, J., Perelló, J., Moreno, Y., Duch, J. and Sánchez, Ángel. “Ghumans display a reduced set of consistent behavioral phenotypes in dyadic games”. Science Advances 2, 1600451 (2016)
      • Álvarez Caudevilla, Pablo, Colorado, E. and Galaktionov, V. “Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrödinger equations”. Nonlinear Analysis: Real World Applications, 23, 78-93 (2015)
      • Álvarez Caudevilla, Pablo and Galaktionov, V. “On a Branching Analysis of a countable family of global similarity solutions of a fourth-order thin film equation”. Electronic Journal of Differential Equations, Vol. 2015, no. 90, 1-29 (2015)
      • Colorado, Eduardo. “Existence of Bound and Ground States for a System of Coupled Nonlinear Schrödinger-KdV Equations”. C. R. Math. Acad. Sci. Paris, 353, no.6, 511-516 (2015)
      • López Lagomasino, Guillermo and Medina Peralta, S. “On the convergence of type I Hermite-Padé approximants”. Advances in Math. 273, 124-148 (2015)
      • A.I. Aptekarev, López Lagomasino, Guillermo and Martínez Finkelshtein, A. “Strong asymptotics for the Pollaczek multiple orthogonal polynomials”. Doklady Mathematics, 465, 393-397 (2015)
      • Kryvasheyeu, Y., Chen H, Moro, Esteban, Van Hentenryck, P. and Cebrian, M. “Performance of Social Network Sensors During Hurricane Sandy”. PLoS ONE 10, 0117288 (2015)
      • Borrego, J. and Pijeira, Héctor. “Differential orthogonality: Laguerre and Hermite cases with applications”. J. Approx. Theory, 196, 111-130 (2015)
      • Rivero, D., Pijeira, Héctor and Assunçao, P. “Edge Detection Based on Krawtchouk Polynomials”. J. Comp. Appl. Math., 284, 244-250 (2015)
      • López-Gómez, J., Molina-Meyer, Marcela and Tellini, A. “Spiraling bifurcation diagrams in superlinear indefinite problems”. Discrete Contin. Dyn. Syst. 35, no. 4, 1561–1588 (2015)
      • Arvesú Carballo, Jorge and Aptekarev, A. “Asymptotics for Multiple Meixner Polynomials”. Journal of Mathematical Analysis and Applications, 411, pp.485-505 (2014)
      • Castro-González, N., Ceballos, J., Dopico, F.M. and Molera, Juan Manuel. “Accurate solution of structured least squares problems via rank-revealing decompositions”. SIAM J. Matrix Anal. Appl. 34, no. 3, 1112–1128 (2013)


      Research group 2

      • R. Vega, M. Carretero, R. D. M. Travasso, and L. L. Bonilla, "Notch signaling and taxis mechanims regulate early stage angiogenesis: A mathematical and computational model". PLoS Computational Biology 16(1), e1006919 (2020) (31 pp).
      • F. Barbero, J. Salas, and E.J.S. Villaseñor, "On the asymptotics of the rescaled Appell polynomials" Advances in Applied Mathematics 113, 101962 (2020).
      • L. L. Bonilla and C. Trenado, "Contrarian compulsions produce exotic time-dependent flocking of active particles". Physical Review E 99, 012612 (2019) (19 pp).
      • E. Mompo, M. Ruiz-Garcia, M. Carretero, H. T. Grahn, Y. H. Zhang, and L. L. Bonilla, "Coherence Resonance and Stochastic Resonance in an Excitable Semiconductor Superlattice". Physical Review Letters 121, 086805 (2018) (6 pp).
      • Z. Z. Shao, Z. Z. Yin, H. L. Song, W. Liu, X. J. Li, J. Zhu, K. Biermann, L. L. Bonilla, H. T. Grahn, and Y. H. Zhang, "Fast Detection of a Weak Signal by a Stochastic Resonance Induced by a Coherence Resonance in an Excitable GaAs/Al(0.45)Ga(0.55)As Superlattice". Physical Review Letters 121, 086806 (2018) (5 pp).
      • J. Essen, M. Ruiz-Garcia, I. Jenkins, M. Carretero, L. L. Bonilla, and B. Birnir, "Parameter dependence of high-frequency nonlinear oscillations and intrinsic chaos in short GaAs/(Al,Ga)As superlattices". Chaos 28, 043107 (2018) (8 pp).
      • S. Iakunin and L. L. Bonilla, “Variational formulation, asymptotic analysis, and finite element simulation of wrinkling phenomena in modified plate equations modeling biofilms growing on agar substrates”. Computer Methods in Applied Mechanics and Engineering. 333, 257-286 (2018).
      • L. L. Bonilla, A. Carpio, M. Carretero, G. Duro, M. Negreanu, and F. Terragni, "A convergent numerical scheme for integrodifferential kinetic models of angiogenesis". Journal of Computational Physics 375, 1270-1294 (2018).
      • F. Barbero, A. Ferreiro, J. Navarro-Salas, and E.J.S. Villaseñor, “Adiabatic expansions for Dirac fields, renormalization, and anomalies”. Physical Review D, 98 (2018)
      • F. Barbero, J. Margalef-Bentabol, and E.J.S. Villaseñor, “On the distribution of the eigenvalues of the area operator in loop quantum gravity”. Classical and Quantum Gravity 35 (2018)
      • M. Carretero, “Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice”. Physical Review E, 96 (2017)
      • J.M. Gambí, M.L. Garcia del Pino, J. Gschwindl, E.B. Weinmüller, "Post-Newtonian equations of motion for LEO debris objects and space-based APT laser systems", Acta Astronautica 141 (2017), pp. 132-142.
      • J. M. Gambí, M.L. Garcia del Pino. “Autonomous shooting at middle size space debris objects from space-based APT laser systems”. Acta Astronautica, 131:83-91 (2017)
      • L. L. Bonilla, “Bifurcation analysis and phase diagram of a spin-string model with buckled states”. Physical Review E, 96 (2017)
      • J. M. Gambí, M.C. Rodriguez-Teijeiro, and M.L. Garcia del Pino. “Newtonian and post-Newtonian passive Geolocation by TDOA”. Aerospace Science and Technology, 51:18-25 (2016)
      • L.L. Bonilla, A. Carpio, C. Gong, and J.H. Warner, "Measuring strain and rotation fields at the dislocation core in graphene". Physical Review B 92, 155417 (2015) (17 pp).




    Thesis defense

    The doctoral thesis consists of an original research work developed by the Ph.D. candidate student in the field of knowledge of the program that enables the student for autonomous work in the field of R+D+ i.

    Universidad Carlos III de Madrid through the Doctoral School establishes the follow-up procedures to guarantee the quality of the doctorate's training and supervision. It also facilitates the procedures for the proper evaluation and defense of the doctoral thesis.

    The Academic Committe of the Doctoral Program in Mathematical Engineering has determined that, in order to accept a PhD thesis in the article compendium format, it will be mandatory to feature two articles published in journals indexed in the Journal Citation Report and a third article that has been submitted and has enough quality to be accepted, applicable from February 5th 2024 (as per Resolución by the Academic Committe)

    Further information:

    • Ph.D. Studies Overview
      Información Práctica de los Estudios de Doctorado


      Our Ph.D. programs focus on the acquisition of skills and abilities required to undertake high-quality research work within the strategic framework and lines of research of the university. Students will be expected to work independently under supervision and guidance of top experts in their fields in order to produce novel, groundbreaking research work in the form of a dissertation.

      The Ph.D. thesis constitutes the expected outcome of the doctoral training, stating the specifics of the research work and results. The thesis must meet the high-quality standards required by the Ph.D. program and be subject to public defense and assessment by an independent thesis committee.

      A favorable assessment of the thesis enables Ph.D. students to request their official Ph.D. degree certificate, issued by the Spanish Ministerio de Educación, Cultura y Deporte.


      Doctoral training calendar 

      Duration of the academic year: October 1st through September 30th

      Process Period
      Admission According to the start semester of the PhD:

      Second semester of the 23/24 academic year
      Admission application deadline: September 1st 2023 through January 31st 2024 (23:59 h., CET) 
      PhD start date: March 30th 2024

      First semester of the 24/25 academic year
      Admission application deadline: February 1st through August 31st 2024 (23:59 h., CET) 
      PhD start date: November 15th 2024
      Enrollment According to the start semester of the PhD:

      Enrollment period for new students
      First semester: July 24th through 30th and September 1st through 30th (23:59 h., CET) of the current academic year
      Second semester: March 1st through 30th (23:59 h., CET) of the current academic year

      Enrollment period for continuing students
      September 1st through 30th (23:59 h., CET) of the current academic year
      Annual Assessment  June
      All PhD candidates are subject to annual evaluation.

      Only students whose June evaluation was unfavorable are subject to evaluation. 

      In both cases the evaluation is based on the progress of the thesis project (Reseach Plan) and the doctoral activities carried out during the academic year.
      Thesis Defense Thesis defense can be carried out throughout the academic year.
    • Procedures
    • FAQ

      Ph.D. Studies

      Parque de las Moreras

      What is a Ph.D.?

      A Ph.D. is a period of training in skills and abilities required to undertake independent, high-quality research work in the realm of R&D under the supervision of top experts in their respective fields.

      What are the terms of access to a Ph.D. program?

      As a general rule, candidates are required to hold a Bachelor’s and a Master’s degree. Credits for both must amount to at least 300 ECTS credits.

      Additionally, specific requirements and candidate profiles are described in each program’s terms of access. Before applying for admission, it is strongly recommended to take the  Ph.D. Programs into consideration, as well as its lines of research, profiles of the scholars involved and final results (theses and scientific publications) as proof of the program’s quality and specialization.

      Shat is the duration of a Ph.D.?

      The regular duration of a full-time Ph.D. program is 4 years. This period can be extended up to 5 years.

      The regular duration of a part-time Ph.D. program is 7 years. This period can be extended up to 8 years. 

      You may apply, for justified reasons, for either an extension or a leave of absence from your Ph.D. training period to the Academic Committee of your program. Your request must be endorsed by your tutor/advisor. Further information:  Duration of Ph.D. studies

      Can I do my Ph.D. entirely online?

      No. All Ph.D. Programs require some face-to-face activity throughout the training period. The duration of face-to-face activity is established by each Program.

      How can I apply for a part-time enrollment status?

      You can state your part-time enrollment status upon admission or, once you have initiated your training period, by submitting a request for justified reasons to the Academic Committee of your program. Your request must be endorsed by your tutor/advisor. Further information:  Enrollment status for Ph.D. studies

      If you are the recipient of a pre-doctoral contract with the UC3M, you must be a full-time student for the entire duration of the contract in application of article 21 of Law 14/2011, of  the1st of June, on Science, Technology and Innovation.

      Must I take any other training in addition to my research work?

      Yes. There are three different types of additional training to be taken during your Ph.D.:

      • Complementary training. Applicable only to students whose terms of admission state this training as required.
      • Specific training. Activities within the framework of your Ph.D. program.
      • Research Skills training. Courses or activities focused on abilities common to all disciplines (communication, academic writing, stress management, etc.).

      Further information on Doctoral Training: Monitoring and Development of these FAQ.

      A favorable assessment enables students to apply for their official Ph.D. degree certificate issued by the Spanish Ministerio de Educación, Cultura y Deporte. An additional Doctorado Internacional distinction is awarded to students who met a number of specific requirements during their training period.

      What is an Interuniversity Ph.D.?

      Interuniversity PhDs are joint degree programs by Universidad Carlos III de Madrid in collaboration with other Spanish or international institutions. The outcome of these programs does not translate into multiple degrees but just one equivalent to the training undertaken by the student.


      How can I apply for admission to a Ph.D. program?

      Your application for admission must be submitted online. Signing in is previously required in order to get your login and password. Further information on how to carry out this process:  Apply for admission

      I have not completed my Master’s degree yet. May I apply for admission now?

      Yes. However, in the event of a favorable resolution of admission, it will be conditioned to your Master’s degree completion.

      When can I apply for admission?

      Applications for admission for the first semester of the 24/25 academic year with start date on the 15th of November 2024 can be submitted from February 1st through August 31st 2024 (Spanish peninsular time, CET)*

      Applications for admission for the second semester of the 24/25 academic year with start date on the 30th of March 2025 can be submitted from September 1st 2024 through January 31st 2025 (Spanish peninsular time, CET)*.

      *Except where noted in the details of each Ph.D. Program.

      The PhD academic year begins on October 1st and ends on September 30th. 

      What documents do I need to submit?

      Scan in advance, in pdf format, the documentation requirements to be attached to your application. The documents listed below are mandatory in all cases:

      • National Identity Document: DNI, NIE, or passport
      • Previous degree certificate or diploma (Master’s degree or equivalent), or proof of payment of issuance fees. 
      • Academic transcript of previous degree (Bachelor's and Master’s degree or equivalent), including grades
      • Curriculum Vitae
      • Authorization of disclosure of educational and employment information
      • Ph.D. research proposal
      • Endorsement for thesis project

      Some programs may require additional documents, such as reference letters by notable researchers, foreign language skills certificate, etc.

      Can I choose when to start my doctoral training?

      Yes. As a new student, you must state in your application for admission whether you want to start your training in the first semester (November 15) or second semester (March 30).

      I want to apply for a scholarship or financial aid program. Must I do it before or after applying for admission to a Ph.D.?

      It is strongly recommended to apply first for your Ph.D. program of choice at uc3m, as most of the granting institutions require proof of admission (or application for admission) to a Ph.D.

      Further information on Scholarships and Financial Aid Programs of these FAQ.

      I submitted my application. When will I know if I am admitted?

      The review process of your application consists of two stages:

      • Administrative validation. Your application will be reviewed at the Doctoral School Office on campus to ensure that it meets the admission requirements. You will be contacted if necessary.
      • Academic evaluation. If your application has succesfully passed the previous stage, it will be forwarded to the Academic Committee of the Ph.D. program for review. You will be notified of the Committee's decision by certified mail sent to the postal address provided in your application.

      This process may take up to one-two months. You will be notified of the Committee’s resolution by e-mail.

      I have been admitted. When must I submit my enrollment form?

      In you are admitted to a Ph.D. program, you have to submit your online application for enrollment in the periods set by the university to that effect, according to the instructions indicated in your letter of admission, our website or the Enrollment section of this FAQ, including the payment of tuition fees. If you do not submit your enrollment for the academic year for which you were admitted, your admission will be cancelled.

      Doctoral training scholarships. Exemptions

      Campus Getafe

      What types of financial aid programs can I apply for?

      There is a wide variety of financial aid programs for doctoral training that cover partial or total tuition fees and, in some cases, allow uc3m to formally hire the Ph.D. student as a training researcher.

      Who are the awarding bodies?

      Here is a list of the most common scholarship and financial aid programs:

         - Formación de Investigadores del Ministerio de Innovación / Researchers Training by Ministerio de Innovación (formerly known as FPI scholarships)
         - Formación de Profesorado Universitario del Ministerio de Educación / University Faculty Training by Ministerio de Educación (formerly known as FPU scholarships)
         - Researchers Training by Universidad Carlos III de Madrid, awarded by the institution departments
         - Ph.D. Scholarships by La Caixa
         - Ph.D. Scholarships by Comunidades Autónomas (Autonomous Regions of Spain)
         - Scholarships by Fundación Carolina (for Latin American students)

      Further information:  Doctoral Training Scholarships

      When and how can I apply for these?

      Each granting body has its own application and awarding periods. It is strongly recommended to apply first for your Ph.D. program of choice at uc3m in all cases, as most of these institutions require proof of admission (or application for admission) to a Ph.D.


      Do I have to be admitted to a Ph.D. in order to apply for admission?

      It is not required in most cases, but, as pointed out previously, you must have at least submitted your application for admission in order to be eligible (check the awarding institution’s specific terms). Only if you are eventually granted the scholarship or financial aid will it be required to be admitted and enrolled on the program in order to accept the aid and be hired as a training researcher at uc3m.


      I received a scholarship or financial aid. Do I have to notify uc3m?

      Yes. As a recipient of any financial aids, it is recommended to notify the university for these to be applied upon enrollment. If your scholarship status is not registered in your self-enrollment application, please contact the Doctoral School Office, either in person or by e-mail at


      Where will I undertake my Ph.D. research work?

      Your research and teaching activities (when applicable) will be carried out at the department or Institute stated in your contract within the framework of your Ph.D. program under the supervision of the tutor and advisor(s) appointed by the Academic Committee.

      Who is in charge of managing my scholarship or financial aid program?

      Granting institutions usually delegate on uc3m the management of these aids according to the terms originally established by those and our own rules and regulations.


      Who is to evaluate the progress and outcomes of my research work?

      All our Ph.D. students must submit the progress of their research work for evaluation by the Academic Committee of their Ph.D. program. Recipients of any financial aid program must also provide this information to the granting body.


      Are there any other tuition fees exemptions?

      Yes. As a new student, if you are eligible for any of the following exemptions or discounts recognized by the Spanish administration, you must submit certified copies of the pertinent documents to the Postgraduate Office on campus before enrollment proceedings so that these exemptions apply upon enrollment.

      • Large Family status: Certified copy of the Large Family status card (general or special)
      • Disability: Certified copy of Disability Identification card (minimum 33% disability)
      • Other: Certified copy of proof of exemption for victims of terrorist attacks (including their spouses and children) or children of civil and military servants who perished in the line of duty.

      These documents must be valid for the academic year for which the exemption is requested.


      How to enroll

      Our Ph.D. Management platform allows to process your enrollment online. To access the platform, enter your UC3M username and password.

      When to enroll               

      New students can choose the start date of the Ph.D. studies. Enrollment period varies accordingly:

      Students starting first semester:

      • Enrollment period: July 24 through 30 and September 1st through 30th (23:59 h., Peninsular Spanish time)
      • Start date of Ph.D. training: November 15 

      Students starting second semester*:

      • Enrollment period: March 1st through 30th (23:59 h., Peninsular Spanish time)
      • Start date of Ph.D. training: March 30

      *In these cases, students benefit from a reduced tuition fee, applicable only for first-year enrollment.

      Your start date will determine the length of your Ph.D. training period.

      As a continuing student, the enrollment period is September 1st through 30th (23:59 h., Peninsular Spanish time) of each academic year.

      What modules should I register on my application?

      You must select the following modules of your enrollment application:

      • Ph.D. Monitoring for your doctoral training year. 

      Required in all cases. It will be registered by default in your application. 

      • Complementary credits.

      Only applicable if the Academic Committee of your program established these credits as obligatory in its admission resolution, in which case you have been properly notified in your admission letter. These credits will be registered by default in your application.

      Other activities of your doctoral training may not require enrollment. If so, our Doctoral School Office is in charge of the registration process:

      • Specific training: Activities included in the curriculum of your Ph.D. program. 
      • Research Skills training: Only required for students of some Ph.D. programs.  

      What are the costs of tuition fees?

      These are the tuition fees for all your Ph.D. training:

      1. Academic fees

      Academic monitoring of Ph.D. training year.  

      • Ordinary fee (full-time, starting first semester): 390 €.
      • Reduced fee* (full-time, starting second semester): 234 €.
      • Reduced fee (part-time, starting first or second semester): 234 €.

                  *Full fees will apply in subsequent years.

      Training credits

      • Complementary training (only for students who are required to take these credits as established in their resolution of admission). If the subjects are the same as subjects from an official degree, the price will be the same as in the original degree. The prices range from € 45,02 to € 80-150 €, depending on the master's program and the doctoral year of enrollment (first, second or subsequent).
      • Research Skills training courses. 45,02 € per credit. Credits from other institutions also require an enrollment at UC3M . A reduced 25% fee will apply in these cases (11,25 € per credit).

      Thesis defense. 143,15 €

      Ph.D. Degree Certificate. 229,86 €

      1. Administrative fees
      • Registrar’s Office expenses. 6,11 €
      • Academic record proceedings (first-year students only). 27,54 €
      1. School insurance. 1, 12 €. Applicable to Spanish or international students (legal residents) under 28 years of age.

      Students who fail to fulfill the payment of these fees will be dismissed from the Ph.D. program.

      Further information:  Tuition fees

      How do I validate my first-year enrollment?

      Upon completion and payment of your enrollment, the Doctoral School will get in touch with you and set an appointment to provide the original documents to have your enrollment validated in compliance with the access requirements to Ph.D.


      According to your previous studies, the documents to be submitted are listed below: 

      1. If you have taken an official Master's degree at UC3M, you are not required to submit any documents. The Doctoral School will check your records accordingly.

      2. If your access degree for Ph.D. was issued by a University from Spain or a European Union country, or a state of the European Economic Area or Switzerland, it is required to provide the following original documents: 

      • Access degree certificate for Ph.D. (Master's degree or equivalent) or payment receipt of issuance fees.
      • Grades certificate of access degree to Ph.D. (Master's degree or equivalent).

      3. If your access degree for Ph.D. was issued by a University from a country other than the ones indicated above, it is required to provide the following legalized documents:

      • Access degree certificate for Ph.D. (Master's degree or equivalent) or payment receipt of issuance fees.
      • Grades certificate of access degree to Ph.D. (Master's degree or equivalent).

      There are different ways to have your documents legalized. Find which legalization procedure applies in your case:  Legalization of Foreign Degrees

      Please note that the legalization procedure must be carried out from the home country. It is strongly recommended to do it in advance. 

      Original hard copies of the documents must be provided along with their photocopies. The Doctoral School will check both originals and their copies and have them certified. If the degree certificates and documents have an electronic signature or digital certification (with safe verification codes), these will be submitted by e-mail at

      All documents must be submitted in Spanish, English, French, Italian or Portuguese (certificates and degrees provided in other languages must have attached an official Spanish translation).  

      The submission period will be notified by e-mail within a month after the end of the enrollment period.

      What are my rights and obligations as a uc3m student?

      Please refer to the following documentation issued by the regional authorities and uc3m. All of them apply to Ph.D. candidates at Uc3m.

      • Students Statute of the Region of Madrid (Estatuto del estudiante de la Comunidad de Madrid)
      • uc3m students Rights and Obligations (Carta de los derechos y deberes del estudiante en la uc3m)
      • Rules and Regulations of the Doctoral School at uc3m (Reglamento de la Escuela de Doctorado de la uc3m)
      • Good Practices of the Doctoral School at uc3m (Código de buenas prácticas de la Escuela de Doctorado de la uc3m)

      Additionally, you have access to the university's support services to students and researchers.

      Further information:  Rules and Regulations

      Ph.D. Studies: Monitoring and Development

      Biblioteca María Moliner

      How are my Ph.D. supervisors appointed?

      Ph.D. tutors and advisors are advanced members of the uc3m faculty or other research institutions who serve as mentors of your research work and keep track of your progress. They also facilitate your communication with the Academic Committee of the program.

      Tutors are appointed by the Committee upon your admission. Tutors must hold a Ph.D. degree and have ties with the program, as well as a proven track record in research of at least six years (or proof of equivalent qualifications).

      The Committee will also appoint an advisor within three months from initial enrollment on the program. Thesis advisors must hold a Ph.D. degree and have a proven track record in research of at least six years (or equivalent qualifications), as well as specific research experience in the field of your thesis. Advisors' may be based at any university, center or institute in Spain or abroad. A professor may be appointed as both tutor and advisor of a Ph.D. student.

      The Academic Committee may change these designations throughout your doctoral training period for justified reasons.

      Must I take any other training in addition to my research work?

      Yes. There are three different types of additional training to be taken during your Ph.D.:

      • Complementary training. Maximum: 40 ECTS credits. Applicable only to students whose terms of admission state this training as required. The Academic Committee will determine the credit-based courses or subjects in the admission resolution. As a general rule, this training must be taken during the first year.
      • Specific training. Students are also expected to participate in a number of activities relevant to their field of research: seminars, meetings, conferences, courses, etc. These activities may require prior enrollment at uc3m. Your tutor or advisor will confirm the contents of your specific training program.
      • Research Skills training. Some Ph.D. programs at uc3m require training in research skills focused on abilities common to all disciplines (communication, academic writing, stress management, etc.). These credits can be earned at either uc3m or other institutions and require formal enrollment at uc3m in all cases, as well as the approval of your tutor or advisor.

      How is the progress of my research evaluated?

      The Academic Committee of your program will evaluate the progress of your research project and activity report on an annual basis in the month of June. Grounds for evaluation are to be registered in the following documents:

      • Research Plan. Not to be mistaken for the research proposal submitted when applying for admission. As a new Ph.D. student, you must elaborate an initial Research Plan within the first year of your doctoral training period. This plan will serve as a tracking tool of your project, listing the objectives and methodology of your research as well as a comprehensible timeline stating the periods estimated for the achievement of each goal. It must have attached your tutor or advisor's evaluation report in order to be submitted for assessment to the Academic Committee of your program.

      An annual update of this Plan must be submitted in subsequent years, with the corresponding tutor or advisor’s evaluation report, so that all parties involved in your doctoral training can track and assess your progress.

      • Activity Report. In addition to your Research Plan (initial or updated), it is also required to register any activity relevant to your Ph.D. research: courses, seminars, meetings, conventions, publications, international fellowship programs, etc. Be sure to have attached all certificates and/or work papers as proof of completion.

      In the event of an unfavorable assessment by the Academic Committee, you will be subjected to evaluation again in December.


      Can I join an international research visit program?

      Yes. Undertaking a period of research abroad is a requirement for Doctorado Internacional distinction eligibility. Among other requirements, your visit must have a minimum duration of three months; also, the report of activities and outcomes of your research at the host institution must be written and presented in one of the languages used for scientific dissemination in your field of research (different from any of Spain’s official languages). Prior approval by your tutor/advisor and the Academic Committee of your program is required. The Committee will evaluate your visiting research reports and, if approved, submit your candidacy for the Doctorado Internacional distinction to the Doctoral School Board.

      Thesis defense

      Biblioteca Carmen Martin Gaite

      What is a Ph.D. thesis?

      The Ph.D. thesis is the intended outcome of the doctoral training period. The thesis must give account of the student’s scientific work and meet the quality standards established by the Academic Committee of the program. Theses are defended in a public dissertation event, where they are subjected to assessment by an expert committee.

      As a general rule, Ph.D. candidates must have been enrolled on their program for a minimum period of 24 months before initiating thesis defense proceedings.

      I have approval to proceed to the thesis defense. What are the stages of this process?

      Once you get approval for your thesis defense by your tutor, advisor and Academic Committee, a minimum span of 8 weeks (excluding holiday periods) is usually required to go through these stages:

      1. Plagiarism management procedure
      2. Thesis deposit. Three weeks.
      3. Approval of thesis defense and appointment of Thesis Committee by the Dean of Doctoral School. One week.
      4. Defense session logistics. Three weeks.
      5. Thesis defense

      What is the plagiarism management procedure?

      To ensure compliance with the principles established in the Code of Good Practice for Managing Plagiarism of Ph.D. Theses of the Doctoral School, all theses must be subjected to a plagiarism management procedure prior to the authorization of the defense.

      Once the Academic Committee of your Ph.D. program determines that your research period is done and your thesis is ready for deposit, a pdf file of the thesis will be submitted to the Doctoral School to proceed to the plagiarism management.

      The results of this study will be at the disposal of the members of the thesis committee, should they be requested.

      Further information:  Plagiarism management

      What is the thesis deposit?

      The deposit of your thesis enables UC3M professors and scholars of your field to review your work before the defense. The deposit period is 15 days (excluding August), after which all comments and observations by the experts will be reported to the Academic Committee and yourself. 

      Further information:  Thesis deposit

      Who approves the defense?

      Once your thesis has successfully passed both stages, the Academic Committee of the program will elaborate their proposal for thesis defense, providing details of the proposed members of the Thesis Committee on the Authorization of thesis defense and appointment of Thesis Committee. Eligibility for “Doctorado Internacional”, “Doctorado Industrial” or International Cotutelle must be indicated, where applicable.

      This proposal will be submitted for the Dean of the Doctoral School's approval of the thesis defense and the appointment of Thesis Committee members.

      Who can be a member of the Thesis Committee?

      The Thesis Committee consists of three members (President, Secretary, and a spokesperson) and a substitute. All of them must hold a Ph.D. degree and a proven track record in research. In all cases, the Committee will be formed by a majority of members external to the University and to the institutions collaborating with the School or the Ph.D. Program.

      Further information:  Defense session. Appointment of Committee members

      How is the thesis defense organized?

      Once all authorizations are signed, the Thesis Committee’s Secretary will appoint a date for the defense. The Doctoral School Office on campus will be in charge of the logistics of the event (room reservations, technical equipment, etc.) and the travel procedures of the committee members, when applicable.

      Additionally, the Postgraduate Office will submit a digital copy of the thesis to each member of the Thesis Committee at least 15 days prior to the defense session. This file will contain any allegation or comment submitted by the experts during the deposit period.

      Further information:  Defense session. Appointment of Committee members

      Do I have to pay any fees before the defense?

      Yes. The payment of thesis defense fees must be fulfilled before proceeding to defense. Additionally, payment of enrollment fees for the academic year in which the defense takes place must be up to date.

      How is my thesis assessed?

      All Committee members must receive a copy of the thesis 15 days prior to the defense event.

      Once the Ph.D. candidate completes his/her dissertation, the Committee can provide feedback or pose questions. Their global assessment will be given in terms of Fail (No Apto), Pass (Aprobado), Good (Notable) or Excellent (Sobresaliente).

      Theses with an Excellent (Sobresaliente) grade are eligible for the cum laude distinction. The committee members will subsequently cast their votes via separate secret ballot in closed session. Only if all votes are favorable will the committee submit their proposal for the thesis to be awarded the cum laude distinction to the university Chancellor. In this case, each member of the committee will finally cast their vote, anonymously and in a sealed envelope, for the thesis to be considered for the Outstanding Thesis Award by Universidad Carlos III de Madrid.

      How can I apply for my Ph.D. certificate?

      Your application for the official Ph.D. degree certificate and the payment of the corresponding fees is done online.

      Issuance of your certificate may take a few months. Until then, you may apply for a temporary certificate as proof of completion of your Ph.D. studies as of the date of your thesis defense.

      Where is my Ph.D. thesis published?

      Your thesis will be published in e-archivo, the open online repository of Universidad Carlos III de Madrid, and Teseo the Ph.D. database managed by the Ministry of Universities. In the event of partial or temporary restrictions pertaining to the publication of your thesis, you must report them to the university.

      Glossary of terms

      Ph.D. Program. Array of training and activities oriented to the acquisition of abilities required to undertake autonomous research work in the realm of R&D. Each Ph.D. program establishes their own procedures and lines of research for the development of theses within the framework of their respective fields.

      Academic Committee. The coordinator/director of the program and two other Ph.D. members constitute a program's Academic Committee, the body in charge of the various training areas and research progress of the program, as well as the authorization of thesis defense of their Ph.D. candidates.

      Doctoral School. Academic body in charge of the management and coordination of all Ph.D. programs.

      Ph.D. Thesis. Original piece of research carried out by Ph.D. candidates in their field of knowledge. Presented as a written dissertation according to the quality, content and format guidelines set by the Ph.D. program for its public defense.

      Tutor. Supervisor in charge of tracking the training progress of the Ph.D. candidate and serving as a communication link between the researcher and the Academic Committee. Tutors must be attached to uc3m faculty with a proven research track record. Tutors are appointed upon approval of admission by the Academic Committee.

      Thesis advisor. Supervisor in charge of tracking the training progress of the Ph.D. candidate. Advisors are experts in the field of the Ph.D. candidate's research, not necessarily attached to uc3m faculty (if they are, they can also be appointed as tutors). Advisors are appointed within the first three months of the student's Ph.D. training period. A student may have more than one advisor.

      Specific training. Specific activities pertaining to the field of research of each Ph.D., designed to provide students with the knowleddge and opportunity for debate required for the development of their research work: seminars, meetings, conferences/dissertations, international research visits, etc.

      Research Skills training. Training activities oriented to the acquisition of skills common to all disciplines. All students are required to earn at least 6 credits (60 hours) throughout their doctoral training period. Enrollment on these courses is performed separately from their regular doctoral training.

      Complementary training. Maximum 40 ECTS credits. Training that the Academic Committee may deem necessary in their admission resoluction in order to complement the Ph.D. candidate's previous academic background. Enrollment on these credits will be required in addition to the student's regular doctoral training. These credits are usually earned during the first Ph.D. year. 

      Research plan. Document to be drafted within the first six months of Ph.D. training detailing the student’s research project to be subjected to annual evaluation every month of June. It must be approved by the tutor, the thesis advisor and the Academic Committee. This plan must be updated and submitted for review and evaluation purposes on a yearly basis.

      Ph.D. Activity report. A registration account of all training activities pertaining to the Ph.D. student's research. The tutor and thesis advisor must endorse these activities for them to be submitted to the Academic Committee for annual evaluation in June. 

      Student record. Academic details of every Ph.D. student as registered in uc3m databases, including activities and credits completed. This information is to be attached to the thesis in the final stages of defense approval.

      Academic transcript. Official document signed by the Head of Doctoral Studies certifying a student's academic record.

      Monitoring and assessment. Annual process by which the research progress and activities of a Ph.D. candidate are subjected to evaluation by the Academic Committee.

      Written Agreement. Document signed by all parties involved in a thesis research project (Ph.D. student, tutor, advisor/s, and Academic Committee) stating their roles and specific conditions pertaining to confidentiality agreements, copyright or use and distribution of research outcomes, where applicable, as well as conflict resolution procedures.

      Thesis public review. Procedure required to allow the academic community to review the student's thesis and issue comments and observations prior to the defense. The thesis is usually deposited at the university's intranet.

      Thesis defense. Academic event open to the public in which Ph.D. candidates defend their research work before a committee of experts in their field. The defense is followed by a question and answer session led by the defense committee in order for it to give their assessment.

      Defense committee. Committee consisting of three experts with proven track records of research in the field of the thesis, most of which must be based outside uc3m. The committee gives their assessment of the thesis and awards the cum laude distinction and the Outstanding Thesis Award candidacy, where applicable.

    • Itinerary
      Itinerario Estudiante de Doctorado
    • Regulations
    • Quality


      Implementation Year: 2012-2013


      The Academic Committee of the Ph.D. complies with the SGIC-UC3M. It is responsible for the quality analysis of the program and produces the Degree Reports ("Memoria Académica de Titulación").



    Bienvenida Universidad Carlos III de Madrid

    Doctoral School Office | Leganés Campus

    Rey Pastor Building, Office 3.0.B.08
    Avenida de la Universidad, 30
    28911 Leganés (Madrid)