Escuela Internacional de Doctorado

Coordination
PhD. Ángel del Río Mateos
Faculty of Mathematics
E-mail: adelrio@um.es
Tel.: +34 868 88 3537
Fax: +34 868 88 4182

General Information
Presentation

The program is mainly addressed to graduates in Mathematics or Statistics who completed a master's degree in these disciplines. Students with other degrees (such as Information Technology, Economics, Engineering, etc.) may also be accepted provided they have completed a master's degree in Mathematics or Statistics and are admitted to the selection process. With regards to selection, the Master’s degree in Advanced  Mathematics taught at the University of Murcia is the ideal one as it offers and introduction to some of our programme research lines.
The Doctoral Program in Mathematics of the University of Murcia has trained a good number of doctors and has received the Quality Mention every year since that mention was established in 2003. In addition, the programme was distinguished in 2011 (BOE 20/10/2011) with the Mention towards Excellence, which proves the quality of our teaching staff and the theses carried out by our students. This is our main asset.
A priori, it is not easy to evaluate the practical interest that basic and fundamental research like ours may have. Research in this field is considered essential in all developed countries, it gives rise to applications in a wide range of fields and still, it is a priori impossible to identify future applications. However, as an example, in addition to the applications of theoretical and applied mathematics and statistics, our programme research lines may potentially be applied to Risk Theory, Cryptography, Computer Sciences, Discrimination Genetics in Medicine, Survival Analysis, Theory of Reliability, Localization and Transportation, Unified Field Theory and Particle Models, General Relativity, Image Design and Analysis, etc. The large number of active research projects lead by our teachers and researchers evidence the validity of these applications and their connection with R+D+I actions in the professional scientific sector.
Spanish and English are the official languages in the programme. However, students who do not master any of these languages ​​may be admitted whenever the Academic Commission agrees and suitable tutors are available. Specific language training activities will also be offered whenever possible through the International School of Doctoral Studies ​.
Our researchers maintain relationships with many research teams and networks both in Spain and abroad, as evidenced by the large number of joint publications. These relationships allow students to chose among a large number of training opportunities i.e. stages in other centers, international theses or specialized training through visiting professors.
The PhD Program in Mathematics is integrated in the International School of Doctoral Studies of the University of Murcia (EIDUM), which contributes to better train our students and to increase the potential applications of our research with the collaboration with other research teams in the School. Worthy to mention are the extensive relationships between our researchers and other world-wide recognised research teams and the possibilities these relationships offer to enrich and complete students training.
The PhD Program in Mathematics is taught at the Faculty of Mathematics, 15th building, Campus Espinardo, University of Murcia, Spain.
Programme guidelines
•    Research teams and lines
•    Training activities
•    Training complements
•    Access profile and admission criteria
•    Academic Commission

Research teams and lines
•    Research team. Algebra
•    Research team. Differential and convex geometry
•    Research team. Functional analysis and dynamical systems
•    Research team. Stochastic models and statistical inference
•    Research team. Operational research

Research Team. Algebra
Research line: Homological Algebra
Teachers-Researchers
PhD. Saorín Castaño, Manuel. Position: Professor
PhD. García Hernández, José Luis. Position: Professor
PhD. Guil Asensio, Pedro Antonio. Position: Full teacher/researcher
PhD. Estrada Domínguez, Sergio. Position: Full teacher/researcher
PhD. Nicolás Zaragoza, Pedro. Position: Contracted Doctor.

Research line: Codes and Cryptography
Teachers-Researchers
PhD. Del Rio Mateo, Ángel. Position: Professor.
PhD. Simón Piñero, Juan Jacobo. Position: Full teacher/researcher.

Research line: Accessible Categories and Model Theory of Modules
Teachers-Researchers
PhD. García Hernández, José Luis. Position: Professor.
PhD. Guil Asensio, Pedro Antonio. Position: Full teacher/researcher
PhD. Estrada Domínguez, Sergio. Position: Full teacher/researcher

Research line: Representations of Algebras
Teachers-Researchers
PhD. Saorín Castaño, Manuel. Position: Professor
PhD. Estrada Domínguez, Sergio. Position: Full teacher/researcher.
PhD. Nicolás Zaragoza, Pedro. Position: Contracted Doctor.

Research line: Representations of Groups and Group Rings
Teachers-Researchers
PhD. Del Río Mateo, Ángel. Position: Professor.
PhD. Simón Piñero, Juan Jacobo. Position: Full teacher/researcher

Research team. Differential and convex geometry

Research line: Brunn-Minkowski Theory and Number Geometry
Teachers-Researchers
PhD. Alías Linares, Luis José. Position: Professor.
PhD. Hernández Cifre, María de los Ángeles. Position: Full teacher/researcher.
PhD. Ferrández Izquierdo, Ángel. Position: Professor.

Research line: Asymptotic Convex Geometry.
Teachers-Researchers
PhD. Alías Linares, Luis José. Position: Professor.
PhD. Hernández Cifre, María de los Ángeles. Position: Full teacher/researcher.
PhD. Ferrández Izquierdo, Ángel. Position: Professor.

Research line: Hypersurfaces of Average Constant Curvature.
Teachers-Researchers
PhD. Pastor González, José Antonio
Position: Full teacher/researcher
PhD. Meroño Bayo, Miguel Ángel
Position: Full teacher/researcher
PhD. Ferrández Izquierdo, Ángel
Position: Professor.
PhD. Alías Linares, Luis José
Position: Professor.

Research line: Subvarieties with Indefinite Metric
Teachers-Researchers
PhD. Lucas Saorín, Pascual. Position: Professor
PhD. Javaloyes Victoria, Miguel Ángel. Position: Ramón y Cajal Researcher at the University of Murcia
PhD. Ferrández Izquierdo, Ángel. Position: Professor.
PhD. Alías Linares, Luis José. Position: Professor.

Research line: Kaehler and Almost-Hermitian Geometries
Teachers-Researchers
PhD. Ferrández Izquierdo, Ángel. Position: Professor.
PhD. Alías Linares, Luis José. Position: Professor.

Research line: Causality of Space-Time Chance and Finsler Geometry
Teachers-Researchers
PhD. Ferrández Izquierdo, Ángel. Position: Professor.
PhD. Alías Linares, Luis José. Position: Professor.
PhD. Guerrero García, Julio. Position: full teacher/researcher.
PhD. Javaloyes Victoria, Miguel Ángel. Position: Ramón y Cajal researcher at the University of Murcia.

Research team. Functional analysis and dynamical systems
Research line: New Techniques of Set Theory and Combinatorics  in Functional Analysis
Teachers-Researchers
PhD. Orihuela Calatayud, José. Position: Professor.
PhD. Raja Baño, Matías. Position: Full teacher and researcher.
PhD. Avilés López, Antonio. Position: Ramón y Cajal contracted researcher at the University of Murcia

Research line: Vector and Multifunction Integration in Banach Spaces and Applications
Teachers-Researchers
PhD. Cascales Salinas, Bernardo. Position: Professor.
PhD. Pallarés Ruiz, Antonio. Position: Full teacher/researcher
PhD. Rodríguez Ruiz, José. Position: Full teacher/researcher
PhD. Avilés López, Antonio. Position: Ramón y Cajal contracted researcher at the University of Murcia

Research line: New Trends in Topology and Measure in Functional Analysis
Teachers-Researchers
PhD. Cascales Salinas, Bernardo. Position: Professor.
PhD. Orihuela Calatayud, José. Position: Professor.
PhD. Pallarés Ruiz, Antonio. Position: Full teacher/researcher.
PhD. Raja Baño, Matías. Position: Full teacher/researcher.
PhD. Garrigós Aniorte, Gustavo: Full teacher/researcher.
PhD. Rodríguez Ruiz, José. Full teacher/researcher.
PhD. Avilés López, Antonio. Ramón y Cajal contracted researcher at the University of Murcia.

Research line: Convex Analysis in Banach Spaces and its Applications in Finance
Teachers-Researchers
PhD. Cascales Salinas, Bernardo. Position: Professor
PhD. Orihuela Calatayud, José. Position: Professor.
PhD. Raja Bath, Matías. Position: Full teacher and researcher.

Research line: Fourier Analysis
Teachers-Researchers
PhD. Garrigós Aniorte, Gustavo. Position: Full teacher and researcher.

Research line: Wavelets
Teachers-Researchers
PhD. Garrigós Aniorte, Gustavo. Position: Full teacher and researcher.
PhD. Rodríguez Ruiz, José. Position: Full teacher and researcher.

Research line: Discrete Dynamical Systems
Teachers-Researchers
PhD. Balibrea Gallego, Francisco. Position: Professor.
PhD. Jiménez López, Víctor. Position: Professor.
PhD. Linero Bas, Antonio. Position: Full teacher and researcher.

Research line: Differential Equations
Teachers-Researchers
PhD. Esquembre Martínez, Francisco. Position: Professor.
PhD. Balibrea Gallego, Francisco. Position: Professor.
PhD. Jiménez López, Víctor. Position: Professor.

Research line: Difference Equations
Teachers-Researchers
PhD. Jiménez López, Víctor. Position: Professor.
PhD. Linero Bas, Antonio. Position: Full teacher and researcher.
PhD. Balibrea Gallego, Francisco. Position: Professor.

Research line. Modeling and Simulation
Teachers-Researchers
PhD. Esquembre Martínez, Francisco. Position: Professor.
PhD. Balibrea Gallego, Francisco. Position: Professor.

Research Line: Numerical Analysis of Partial Differential Equations
Teachers-Researchers
PhD. Chacón Vera, Eliseo. Position: Full teacher and researcher.
PhD. Balibrea Gallego, Francisco. Position: Professor.

Research line: Non-Linear Analysis in Banach Spaces
Teachers-Researchers
PhD. Balibrea Gallego, Francisco. Position: Professor.

Research line: History of Mathematics
Teachers-Researchers
PhD. Balibrea Gallego, Francisco. Position: Professor.
PhD. Linero Bas, Antonio. Position: Full teacher and researcher.

Research team. Stochastic models and statistical inference
Research line: Classification and Ordination of Systems
Teachers-Researchers
PhD. Ruiz Gómez, José María. Position: Professor.
PhD. Belzunce Torregrosa, Felix. Position: Professor.
PhD. Navarro Camacho, Jorge. Position: Professor.
PhD. Franco Nicolás, Manuel. Position: Full teacher and researcher.
PhD. Vivo Molina, Juana María. Position: Full teacher and researcher.

Research line: Multivariate Ordination and Classification of Vectors with Ordered Components
Teachers-Researchers
PhD. Franco Nicolás, Manuel. Position: Full teacher and researcher.
PhD. Vivo Molina, Juana María. Position: Full teacher and researcher.
PhD. Ruiz Gómez, José María. Position: Professor.
PhD. Belzunce Torregrosa, Felix. Position: Professor.
PhD. Navarro Camacho, Jorge. Position: Professor.

Research line. Dependence in Risk Theory and Reliability
Teachers-Researchers
PhD. Franco Nicolás, Manuel. Position: Full teacher and researcher.
PhD. Vivo Molina, Juana María. Position: Full teacher and researcher.
PhD. Ruiz Gómez, José María. Position: Professor.
PhD. Belzunce Torregrosa, Felix. Position: Professor.
PhD. Navarro Camacho, Jorge. Position: Professor.

Research line: Distributions, Mixture and Classification
Teachers-Researchers
PhD. Franco Nicolás, Manuel. Position: Full teacher and researcher.
PhD. Vivo Molina, Juana María. Position: Full teacher and researcher.
PhD. Ruiz Gómez, José María. Position: Professor.
PhD. Belzunce Torregrosa, Felix. Position: Professor.
PhD. Navarro Camacho, Jorge. Position: Professor.

Research line.  Intrinsic and Integral A Priori Distributions
Teachers-Researchers
PhD. Cano Sánchez, Juan Antonio. Position: Professor.
PhD. Salmerón Martínez, Diego. Position: Associate teacher and researcher.

Research line.  Objective Bayesian Methods
Teachers-Researchers
PhD. Cano Sánchez, Juan Antonio. Position: Professor.
PhD. Salmerón Martínez, Diego. Position: Associate teacher and researcher.

Research team. Operational research
Research line: Location Services
Teachers-Researchers
PhD. Pelegrín Pelegrín, Blas. Position: Professor.
PhD. Fernández Hernández, José. Position: Full teacher and researcher.
PhD. Fernández Hernández, Pascual. Position: Full teacher and researcher.

Research line: Network Analysis, Distribution and Transportation
Teachers-Researchers
PhD. Pelegrín Pelegrín, Blas. Position: Full teacher and researcher.
PhD. Fernández Hernández, José. Position: Full teacher and researcher.
PhD. Fernández Hernández, Pascual. Position: Full teacher and researcher.

Research line: Global Optimization
Teachers-Researchers
PhD. Pelegrín Pelegrín, Blas. Position: Full teacher and researcher.
PhD. Fernández Hernández, José. Position: Full teacher and researcher.
PhD. Fernández Hernández, Pascual. Position: Full teacher and researcher.

Research line: Multi-objective Programming
Teachers-Researchers
PhD. Pelegrín Pelegrín, Blas. Position: Professor.
PhD. Fernández Hernández, José. Position: Full teacher and researcher.
PhD. Fernández Hernández, Pascual. Position: Full teacher and researcher.

Research line:  Game Theory
Teachers-Researchers
PhD. Pelegrín Pelegrín, Blas. Position: Professor.
PhD. Fernández Hernández, José. Position: Full teacher and researcher.
PhD. Fernández Hernández, Pascual. Position: Full teacher and researcher.

Research line: Discrete Optimization
Teachers-Researchers
PhD. Marín Pérez, Alfredo. Position: Professor.
PhD. Fernández Sáez, María José. Position: Full teacher and researcher.
PhD. Pulido Cayuela, Manuel A. Position: Full teacher and researcher.
PhD. Zoroa Alonso, Carmen Noemi. Position: Full teacher and researcher.

Research line: Multi-agent Situation Analysis
Teachers-Researchers
PhD. Marín Pérez, Alfredo. Position: Professor.
PhD. Pulido Cayuela, Manuel A. Position: Full teacher and researcher.

Research line: Cooperative Game Theory
Teachers-Researchers
PhD. Marín Pérez, Alfredo. Position: Professor.
PhD. Pulido Cayuela, Manuel A. Position: Full teacher and researcher.

Research line: Geometric Games
Teachers-Researchers
PhD. Fernández Sáez, María José. Position: Full teacher and researcher.
PhD. Zoroa Alonso, Carmen Noemi. Position: Full teacher and researcher.
PhD. Marín Pérez, Alfredo. Position: Professor.

Research Line: Geometric Probability
Teachers-Researchers
PhD. Marín Pérez, Alfredo. Position: Professor.
PhD. Fernández Sáez, María José. Position: Full teacher and researcher.
PhD. Zoroa Alonso, Carmen Noemi. Position: Full teacher and researcher.

Research Line: Applications of Game Theory to Searching Problems
Teachers-Researchers
PhD. Marín Pérez, Alfredo. Position: Professor.
PhD. Fernández Sáez, María José. Position: Full teacher and researcher.
PhD. Zoroa Alonso, Carmen Noemi. Position: Full teacher and researcher.

Training activities
 
The basic curricular structure of this doctoral programme evolves around the writing of a doctoral thesis with one of our research teams and under the direction of one or several doctors.
Along with the writing of a doctoral thesis, the student will participate in the team’s activities and will attend seminars or courses taught by home or visiting researchers.
Whenever the student's academic background requires complementary training to join a particular research line, the research team will analyse the situation and propose the student to get complementary training by attending some courses included the Master’s in Advanced Mathematics. May it be the case, the complementary training will be compulsory.
The students will also be able to teach seminars on topics related to his/her research work for the doctoral thesis. In addition, students will join related scientific activities, such as conferences on their research topics, visits to other centers for exchanging experiences etc.
These scientific activities will ensure that most of our future doctors obtain a PhD title with International Mention.
Complementary Training
Based on each candidate’s background, the Academic Commission may recommend necessary training supplements for admission. Likewise, tutors might recommend additional training once students are admitted to the program. To this purpose, those introductory subjects to research offered by the Master’s in Advanced Mathematics of the University of Murcia may be recommended, as well as any other resource deemed convenient, including those provided by the International School of Doctoral Studies.
In general terms, the appropriate training complements, in line with our access profiles, could be the following:
P1. Students with a degree in Mathematics who have completed the Master’s degree in Advanced  Mathematics.
Training Complements: You will not need complements or you might need some specific courses offered by EIDUM that are considered necessary for the programme development.
P2. Students with a degree in Mathematics who did not complete the Master’s degree in Advanced Mathematics.
Training complements: students could attend some subjects of the master’s that are considered necessary to fit the requested research profile and the programme objectives.
P3. Students with other degrees who have completed the Master’s degree in Advanced Mathematics.
Training complements: as a rule, these students need no complementary training. If the tutor considers it convenient, students may carry out some of the subjects offered by the bachelor’s degree that are closely related to the requested research profile.
P4. Students with other degrees who have not completed the Master’s programme in Advanced Mathematics.
Training complements: students could complete some subjects of  bachelors’ and / or masters’ programmes considered necessary to fit the requested research profile and for the development of the programme.
The selection of training complements will be jointly agreed by tutors and students, so that the training meets each student’s needs in the doctoral program. As a matter of fact, we could just say the subjects offered by our master’s degree are the most appropriate complementary training to join a particular research line.
The acquisition of skills by means of these training complements will be assessed in each student annual monitoring report.

Access Profile and Admission Criteria
Access requirements

According to the national regulation and to the internal rules at the University of Murcia (Rector Resolution 42/2012 of 6 February and Decree 99/2011) access to doctoral programmes is subjet to the following requirements:
1. For a candidate to access any doctoral programme at the University of Murcia, it is necessary that he/she is in the possession of an official Bacherlor’s degree or equivalent and a Master’s degree.
2. In addition, students who are in any of the following cases may also access:
a. Have an official Spanish university degree, or of another country belonging to the European Higher Education Area, giving access to a Master’s programme and have passed a minimum of 300 ECTS of official university studies, of which, at least 60, must be at Master's level.
b. Have an official Spanish Graduate Diploma with a content, according to the rules of the EU law, of at least 300 ECTS. These graduates must compulsorily complete the training supplements referred to in article 7.2 of Royal Decree 99/2011, of January 28, unless the syllabus of the corresponding degree includes credits in research training that are equivalent in training value to research credits in master's programmes.
c. University graduates who, after obtaining a training place in the corresponding test to access specialized health training, have successfully passed at least two years of training in a programme to obtain the official title of one of the specialties in Health Sciences.
d. Have a diploma obtained in accordance with foreign educational systems –no need to have it officially recognised, after the General Doctorate Commission has verified that this certificate accredits a training level equivalent to that of the official Spanish Master's degree and giving access to doctoral studies in the country where it was issued. This admission does not imply, in any case, nor the official recognition of student’s previous degrees nor its recognition for purposes others than accessing doctoral education.
C. To be in the possession of another Spanish title of doctor obtained according to previous university regulations.
Access Profile
The most suitable profile to access our PhD Program in Mathematics is a graduate in Mathematics or Statistics who has completed a master's degree in Mathematics or Statistics. Specifically, the Master’s degree in Advanced  Mathematics from the University of Murcia (see http://www.um.es/web/matematicas/contenido/estudios/masteres) and any of the research profiles it offers is considered ideal, since it provides an introduction to some of our main research lines.
Admission of students coming from our previous doctoral programs who did not get to complete their doctoral thesis will also be considered a priority, trying, as far as possible, so that they don’t get harmed by the change of regulations.
Admission will be open to other profiles and, if considered convenient, the necessary compensatory actions may be promoted according to each applicant profile. These actions will include both attendance to the training offered by the International School of Doctoral Studies, as well as attendance to some classes of the mentioned masters, conferences, stays, and any other training action that both the tutor and the Academic Commission consider necessary. Summing up, the profiles can be classified as follows:
P1. Students graduated in Mathematics who have completed the Master’s degree in Advanced Mathematics.
P2. Students graduated in Mathematics who have not completed the Master’s degree in Advanced Mathematics.
P3. Students with other bachelor’s degrees who have completed the Master’s degree in Advanced Mathematics.
P4. Students with other degrees who did not complete the Master’s degree in Advanced Mathematics.

Admission Criteria
The admission rules will be based on the applicant’s academic background and will respect equal opportunities and merit evaluation. If considered appropriate, personal interviews or specific admission tests may be conducted.
The bachelor’s and master’s degrees presented to access will be valued, taking into account what said above in “Access Profile”. Priority may be given to students with the Master’s degree in Advanced Mathematics from the University of Murcia or to students from our previous doctoral programs. The obtained scores, the tutor's and director’s recommendations and any additional and relevant merits will also be assessed.
The weightings of the criteria will be as follows:
1. Bachelor’s degrees provided and scores obtained: 40%.
2. Master's degrees and scores obtained: 30%.
3. Recommendations by our teachers and researchers: 20%.
4. Other merits (languages, extracurricular training, scholarships, prizes, familiarization with research, etc.): 10%.
If considered convenient, the Academic Commission may modify, detail or extend these criteria taking into account the data provided by the Quality Assurance System (QMS). These changes will be reported on the program website.
Along the admission process, students will be informed on the need to attend specific training complements. These supplements may also be proposed later on by the tutor, with the Academic Commission’s approval.
Proceedings will include, in the case of students with specific educational needs derived from disability, the appropriate support and counseling services. The need for possible curricular adaptations, itineraries or alternative studies will be considered too.
The admission criteria will be the same for full-time and part-time students.
All relevant information on the admission process will be available on the official website of the program and will be subject to annual review taking into account the reports issued by the System of Quality Assurance.
Number of places available: 25

Regulations and oral defense of doctoral theses (Doctoral Programme in Mathematics)
All Regulations governing the official teaching of Doctoral Programmes (approved by the Governing Board on the 27 January 2012 and amended on the 26 July 2013) can be found in Spanish on: http://www.um.es/web/vic-estudios/contenido/doctorados/tesis

Academic Commission
Coordinator:

·    PhD. Ángel del Río Mateos
Members of the Board:
·    PhD. Félix Belzunce Torregrosa
·    PhD. Sergio Estrada Domínguez
·    PhD. José Fernández Hernández
·    PhD. M. Ángeles Hernández Cifre
·    PhD. Manuel Saorín Castaño
·    PhD. Gustavo Adolfo Garrigós Aniorte
Deputy members:
·    PhD. Ángel Ferrández Izquierdo
·    PhD. Juan J. Simón Piñero
Representative of the International School of Doctoral Studies:
·    PhD. Gregorio Sánchez Gómez
Students representative:
·    PhD. Eduardo Tigeras Gil