Access profile

The doctoral programme in Applied Mathematics is designed for students with abstract reasoning abilities and interest in solving problems, in addition to having good work habits, being dedicated to studying and having a passion for mathematics. Applicants must have a solid background in mathematics. Along this line, the main undergraduate and master’s degrees that will provide access to this doctoral programme are the following:

Undergraduate degrees:
• Bachelor’s degree in Mathematics
• Bachelor’s degree in Physics
Engineering:
• Bachelor’s degree in Computer Science
• Bachelor’s degree in Statistics

Output profile

Doctoral candidates who complete a doctoral degree will have acquired the following competencies, which are needed to carry out quality research (Royal Decree 99/2011, of 28 January, which regulates official doctoral studies):

a) A systematic understanding of the field of study and a mastery of the research skills and methods related to the field.
b) An ability to conceive, design or create, put into practice and adopt a substantial process of research or creation.
c) An ability to contribute to pushing back the frontiers of knowledge through original research.
d) A capacity for critical analysis and an ability to assess and summarise new and complex ideas.
e) An ability to communicate with the academic and scientific community and with society in general as regards their fields of knowledge in the manner and languages that are typical of the international scientific community to which they belong.
f) An ability to foster scientific, technological, social, artistic and cultural progress in academic and professional contexts within a knowledge-based society.

The award of a doctoral degree must equip the graduate for work in a variety of settings, especially those requiring creativity and innovation. Doctoral graduates must have at least acquired the personal skills needed to:

a) Develop in contexts in which there is little specific information.
b) Find the key questions that must be answered to solve a complex problem.
c) Design, create, develop and undertake original, innovative projects in their field.
d) Work as part of a team and independently in an international or multidisciplinary context.
e) Integrate knowledge, deal with complexity and make judgements with limited information.
f) Offer criticism on and intellectually defend solutions.

Finally, with respect to competencies, doctoral students must:
a) have acquired advanced knowledge at the frontier of their discipline and demonstrated, in the context of internationally recognised scientific research, a deep, detailed and well-grounded understanding of theoretical and practical issues and scientific methodology in one or more research fields;
b) have made an original and significant contribution to scientific research in their field of expertise that has been recognised as such by the international scientific community;
c) have demonstrated that they are capable of designing a research project that serves as a framework for carrying out a critical analysis and assessment of imprecise situations, in which they are able to apply their contributions, expertise and working method to synthesise new and complex ideas that yield a deeper knowledge of the research context in which they work;
d) have developed sufficient autonomy to set up, manage and lead innovative research teams and projects and scientific collaborations (both national and international) within their subject area, in multidisciplinary contexts and, where appropriate, with a substantial element of knowledge transfer;
e) have demonstrated that they are able to carry out their research activity in a socially responsible manner and with scientific integrity;
f) have demonstrated, within their specific scientific context, that they are able to make cultural, social or technological advances and promote innovation in all areas within a knowledge-based society;
g) have demonstrated that they are able to participate in scientific discussions at the international level in their field of expertise and disseminate the results of their research activity to audiences of all kinds.

Number of places

20

Duration of studies and dedication regime

Duration
The maximum period of study for full-time doctoral studies is three years, counted from the date of admission to the programme to the date of submission of the doctoral thesis. The academic committee of the doctoral programme may authorise a doctoral candidate to pursue doctoral studies on a part-time basis. In this case, the maximum period of study is five years, counting from the date of admission to the programme to the date of submission of the doctoral thesis. For calculating these periods, the date of admission is considered to be the date of the first enrolment for tutorials, and the date of submission the moment in which the Doctoral School officially deposits the doctoral thesis.

For full-time doctoral candidates, the minimum period of study is two years, counted from the date of an applicant's admission to the programme until the date on which the doctoral thesis is deposited; for part-time doctoral candidates it is four years. When there are justified grounds for doing so, and the thesis supervisor and academic tutor have given their authorisation, doctoral candidates may request that the academic committee of their doctoral programme exempt them from the minimum period of study requirement.

The calculation of periods of study will not include periods of absence due to illness, pregnancy or any other reason provided for in the regulations in force. Students who find themselves in any of these circumstances must notify the academic committee of the doctoral programme, which, where appropriate, must inform the Doctoral School. Doctoral candidates may also temporarily withdraw from the programme for up to one year, and this period may be extended for an additional year. Doctoral candidates who wish to interrupt their studies must submit a justified request to the academic committee of the doctoral programme, which will decide whether or not to approve the request. Each programme will establish conditions for readmission to doctoral studies.

Extension
If full-time doctoral candidates have not applied to deposit their thesis by the end of the three-year period of study, the academic committee of the programme may authorise an extension of up to one year. In exceptional circumstances, a further one-year extension may be granted, subject to the conditions established by the corresponding doctoral programme. In the case of part-time doctoral candidates, an extension of two years may be authorised. In both cases, in exceptional circumstances a further one-year extension may be granted by the Doctoral School's Standing Committee, upon the submission of a reasoned application by the academic committee of the doctoral programme.

Dismissal from the doctoral programme
A doctoral candidate may be dismissed from a doctoral programme for the following reasons:

• The doctoral candidate submitting a justified application to withdraw from the programme.
• The maximum period of study and of extensions thereof ending.
• The doctoral candidate not having enrolled every academic year (unless he or she has been authorised to temporarily withdraw).
• The doctoral candidate failing two consecutive assessments.
• The doctoral candidate having disciplinary proceedings filed against him or her that rule that he or she must be dismissed from the UPC.

Dismissal from the programme implies that doctoral candidates cannot continue studying at the UPC and the closing of their academic record. This notwithstanding, they may apply to the academic committee of the programme for readmission and the committee must reevaluate them in accordance with the criteria established in the regulations.

Organization

• Rue Perna, Juan Jose

• Burillo Puig, Pep
• Franch Bullich, Jaume
• Guardia Munarriz, Marcel
• Huguet Casades, Gemma
• Muñoz Romero, Jose Javier
• Rue Perna, Juan Jose
• Serra Albo, Oriol

• School of Mathematics and Statistics (PROMOTORA)
• Barcelona Supercomputing Center-Centro Nacional de Supercomputación
• Department of Civil and Environmental Engineering
• Department of Mathematics
• Institute of Robotics and Industrial Informatics

Agreements with other institutions

Access profile

The doctoral programme in Applied Mathematics is designed for students with abstract reasoning abilities and interest in solving problems, in addition to having good work habits, being dedicated to studying and having a passion for mathematics. Applicants must have a solid background in mathematics. Along this line, the main undergraduate and master’s degrees that will provide access to this doctoral programme are the following:

Undergraduate degrees:
• Bachelor’s degree in Mathematics
• Bachelor’s degree in Physics
Engineering:
• Bachelor’s degree in Computer Science
• Bachelor’s degree in Statistics

Access requirements

Applicants must hold a Spanish bachelor’s degree or equivalent and a Spanish master’s degree or equivalent, provided they have completed a minimum of 300 ECTS credits on the two degrees (Royal Decree 43/2015, of 2 February)

In addition, the following may apply:

• Holders of an official degree awarded by a university in Spain or any other country in the European Higher Education Area, pursuant to the provisions of Article 16 of Royal Decree 1393/2007, of 29 October, which establishes official university course regulations, who have completed a minimum of 300 ECTS credits on official university degrees, of which at least 60 must be at the master's degree level.
• Holders of an official Spanish bachelor’s degree comprising at least 300 credits, as provided for by EU regulations. Holder of degrees of this kind must complete bridging courses unless the curriculum of the bachelor’s degree in question included research training credits equivalent in value to those which would be earned on a master's degree.
• Holders of an official university qualification who, having passed the entrance examination for specialised medical training, have completed at least two years of a training course leading to an official degree in a health-sciences specialisation.
• Holders of a degree issued under a foreign education system. In these cases, homologation is not required, but the UPC must verify that the degree certifies a level of training equivalent to an official Spanish master's degree and qualifies the holder for admission to doctoral studies in the country where it was issued. Admission on this basis does not imply homologation of the foreign degree or its recognition for any purpose other than admission to doctoral studies.
• Holders of a Spanish doctoral qualification issued under previous university regulations.

Note 1: Doctoral studies entrance regulations for holders of an undergraduate degree awarded before the introduction of the EHEA (CG 47/02 2014)

Note 2: Governing Council Decision 64/2014, which approves the procedure and criteria for assessing the fulfilment of academic admission requirements for doctoral studies by holders of non-homologated foreign degrees (CG 25/03 2014)

Admission criteria and merits assessment

During the admission process, the following elements will be considered (with their associated weights):

• Academic transcript from the applicant’s undergraduate and master’s programmes (70%).

• CV (10%).

• Motivation letter and/or personal interview (10%).

• Two letters of recommendation from professors/researchers (10%).

These criteria will be published on the programme’s web page. The final score will be used as the admission criteria in the case that demand exceeds the number of available seats.

There is no provision for entrance exams or any specific entrance tests. If candidates’ backgrounds in mathematics or the subject of the candidates’ doctoral theses so require, they will be required to take bridging courses in the master’s programme in Advanced Mathematics and Mathematical Engineering (MAMME), the official master’s programme offered by the FME that is associated with this doctoral programme.

Training complements

The academic committee for the programme may require that doctoral students pass specific bridging courses. In such cases, the committee will keep track of the bridging courses completed and establish appropriate criteria to limit their duration. The courses could involve training in research or transversal education, but in no case will candidates be required to enrol in 60 or more ECTS credits.

Depending on the doctoral student activity report, the programme’s Academic Committee may propose measures, in addition to those established by current regulations, that would disassociate candidates who do not meet the established requisites.

Additionally, students who require it based on their previous education and the subject of their thesis, will have to take courses from the master’s programme in Advanced Mathematics and Mathematical Engineering (MAMME) offered by the School of Mathematics and Statistics. A detailed list of the subjects offered is listed hereafter:

Enrolment period for new doctoral students

All up-to-date information can be found on the FME’s web page: https://fme.upc.edu/ca/curs-actual/matricula/estudiants-de-doctorat

More information at the registration section for new doctoral students

Enrolment period

All up-to-date information can be found on the FME’s web page: https://fme.upc.edu/ca/curs-actual/matricula/estudiants-de-doctorat

More information at the general registration section

Procedure for the preparation and defense of the research plan

Doctoral candidates must submit a research plan, which will be included in their doctoral student activity report, before the end of the first year. The plan may be improved over the course of the doctoral degree. It must be endorsed by the tutor and the supervisor, and it must include the method that is to be followed and the aims of the research.

At least one of these annual assessments will include a public presentation and defence of the research plan and work done before a committee composed of three doctoral degree holders, which will be conducted in the manner determined by each academic committee. The examination committee awards a Pass or Fail mark. A Pass mark is a prerequisite for continuing on the doctoral programme. Doctoral candidates awarded a Fail mark must submit a new research plan for assessment by the academic committee of the doctoral programme within six months.

The committee assesses the research plan every year, in addition to all of the other activities in the doctoral student activity report. Doctoral candidates who are awarded two consecutive Fail marks for the research plan will be obliged to definitely withdraw from the programme.

If they change the subject of their thesis, they must submit a new research plan.

Formation activities

Procedure for assignment of tutor and thesis director

The academic committee of the doctoral programme assigns a thesis supervisor to each doctoral candidate when they are admitted or enrol for the first time, taking account of the thesis supervision commitment referred to in the admission decision.

The thesis supervisor will ensure that training activities carried out by the doctoral candidate are coherent and suitable, and that the topic of the candidate’s doctoral thesis will have an impact and make a novel contribution to knowledge in the relevant field. The thesis supervisor will also guide the doctoral candidate in planning the thesis and, if necessary, tailoring it to any other projects or activities undertaken. The thesis supervisor will generally be a UPC professor or researcher who holds a doctoral degree and has documented research experience. This includes PhD-holding staff at associated schools (as determined by the Governing Council) and UPC-affiliated research institutes (in accordance with corresponding collaboration and affiliation agreements). When thesis supervisors are UPC staff members, they also act as the doctoral candidate’s tutor.

PhD holders who do not meet these criteria (as a result of their contractual relationship or the nature of the institution to which they are attached) must be approved by the UPC Doctoral School's Standing Committee in order to participate in a doctoral programme as researchers with documented research experience.

The academic committee of the doctoral programme may approve the appointment of a PhD-holding expert who is not a UPC staff member as a candidate’s thesis supervisor. In such cases, the prior authorisation of the UPC Doctoral School's Standing Committee is required. A UPC staff member who holds a doctoral degree and has documented research experience must also be proposed to act as a co-supervisor, or as the doctoral candidate’s tutor if one has not been assigned.

A thesis supervisor may step down from this role if there are justified reasons (recognised as valid by the committee) for doing so. If this occurs, the academic committee of the doctoral programme will assign the doctoral candidate a new thesis supervisor.

Provided there are justified reasons for doing so, and after hearing any relevant input from the doctoral candidate, the academic committee of the doctoral programme may assign a new thesis supervisor at any time during the period of doctoral study.

If there are academic reasons for doing so (an interdisciplinary topic, joint or international programmes, etc.) and the academic committee of the programme gives its approval, an additional thesis supervisor may be assigned. Supervisors and co-supervisors have the same responsibilities and academic recognition.

The maximum number of supervisors of a doctoral thesis is two: a supervisor and a co-supervisor.

For theses carried out under a cotutelle agreement or as part of an Industrial Doctorate, if necessary and if the agreement foresees it this maximum number of supervisors may not apply. This notwithstanding, the maximum number of supervisors belonging to the UPC is two.

More information at the PhD theses section

Permanence

The academic committee of the programme may authorise an extension of up to one year for full-time doctoral candidates who have not applied to deposit their thesis by the end of the three-year period of study, in the terms outlined in the Academic Regulations for Doctoral Studies of the Universitat Politècnica de Catalunya. In the case of part-time candidates, an extension of two years may be authorised. In both cases, in exceptional circumstances a further one-year extension may be granted by the Doctoral School's Standing Committee, upon the submission of a reasoned application by the academic committee of the doctoral programme.

A doctoral candidate may be dismissed from a doctoral programme for the following reasons:

• The doctoral candidate submitting a justified application to withdraw from the programme.
• The maximum period of study and of extensions thereof ending.
• The doctoral candidate not having enrolled every academic year (unless he or she has been authorised to temporarily withdraw).
• The doctoral candidate failing two consecutive assessments.
• The doctoral candidate having disciplinary proceedings filed against him or her that rule that he or she must be dismissed from the UPC.

Dismissal from the programme implies that doctoral candidates cannot continue studying at the UPC and the closing of their academic record. This notwithstanding, they may apply to the academic committee of the programme for readmission and the committee must reevaluate them in accordance with the criteria established in the regulations.

International Mention

The doctoral degree certificate may include International Doctorate mention. In this case, the doctoral candidate must meet the following requirements:

a) During the period of study leading to the award of the doctoral degree, the doctoral candidate must have spent at least three months at a respected higher education institution or research centre outside Spain to complete courses or do research work. The stays and activities carried out must be endorsed by the thesis supervisor and authorised by the academic committee of the programme. The candidate must provide a certifying document issued by the person responsible for the research group of the body or bodies where the stay or activity was completed. This information will be added to the doctoral student’s activity report.
b) Part of the thesis (at least the summary and conclusions) must be written and presented in one of the languages commonly used for science communication in the relevant field of knowledge, which must not be an official language of Spain. This rule does not apply to stays and reports in Spanish or to experts from Spanish-speaking countries.
c) At least two PhD-holding experts belonging to a higher education institution or research centre outside Spain must have issued officially certified reports on the thesis.
d) The thesis examination committee must have included at least one PhD-holding expert from a higher education or research institution outside Spain who was not responsible for the candidate’s stay abroad (point a) above).
e) The thesis defence must have taken place on UPC premises or, in the case of joint programmes, at the location specified in the collaboration agreement.

List of authorized thesis for defense

• MIRZA, WALEED AHMAD: A theoretical and computational study of the active self-organization of nematic patterns in thin cytoskeleton layers and their effect on curvature.
  
  Author: MIRZA, WALEED AHMAD
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: (DECA)
  Mode: Normal
  Deposit date: 21/12/2022
  Reading date: 16/02/2023
  Reading time: 10:30
  Reading place: Sala d'Actes de l'FME, Edifici U, Campus Sud
  Thesis director: ARROYO BALAGUER, MARINO
  Committee:
       PRESIDENT: TURLIER, HERVÉ
       SECRETARI: ORIOLA SANTANDREU, DAVID
       VOCAL: ERZBERGER, ANNA
  Thesis abstract: The structure and dynamics of important biological systems, ranging from cytoskeletal gels to tissues, are controlled by an interplay between activity, dissipation, nematic order, density, and geometry. In particular, the actin cytoskeleton is remarkably adaptable and versatile and self-organizes into a variety of architectures, notably dense nematic structures. Examples of such structures are contractile rings to accomplish cell division and wound healing, or stress fibers playing an essential role in cell spreading, force generation, and migration. However, the mechanisms leading to dense nematic bundles remain poorly understood and to our knowledge, no prior theory explains their mesoscale self-assembly. Previous hydrodynamic approaches to active nematic systems have focused on incompressible liquid crystals. However, these models are not pertinent to actin gels, which are highly porous and exhibit very large density variations controlling activity gradients and active flows. Furthermore, porous actin networks can exhibit extended isotropic states without defects, and nematic order is presumably induced by flows and active mechanisms rather than by crowding. Finally, little attention has been paid to the formulation of active nematics on deformable surfaces and to a general computational framework to address such complex problems. Finally, we lack a unified understanding of actin network polymorphism, and more specifically of the physical mechanisms that enable a single active material to adopt very different network architectures with distinct cellular functions. To address these challenges, we develop a variety of theoretical and computational models for active nematic gels. In part I of the thesis, we focus on active nematic gels confined to a plane. We develop a transparent modeling framework for density-dependent active nemato-hydrodynamics based on Onsager¿s variational formalism, according to which the dynamics result from a competition between free-energy release, dissipation and activity. We also develop a numerical finite element method based on a time-incremental version of Onsager's formalism, which inherits the nonlinear stability and thermodynamic consistency of the continuum principle. We use this numerical approach to study the assembly of a contractile ring during wound healing and the defect dynamics in a confined colony of contractile cells. We next study the active self-assembly of nematic patterns from a uniform and quiescent gel using linearized theory and nonlinear simulations. We establish the conditions for nematic bundle formation and how active gel parameters control the architecture, connectivity and dynamics of self-organized patterns of nematic bundles. Finally, using discretenetwork simulations, we substantiate the major requirements for active nematic self-organization according to our theory. We thus provide a framework to understand the emergence and dynamics of mesoscale nematic organizations in actin networks. In part II of the thesis, we develop a general model for active nematic gels on deformable surfaces. Again, Onsager's nonlinear formalism provides a simple method to transparently develop complex models. The resulting system tight couples shape dynamics, nematic dynamics, density dynamics, and interfacial hydrodynamics. We exercise this model to understand the self-organization of the cytokinetic ring using an axisymmetric numerical formulation. Finally, we provide a general 3D computational approach and apply it to an inextensible active liquid crystalline deformable surface. We examine the interplay between the motion of nematic defects and shape.
  

Last update: 27/01/2023 05:45:11.

List of lodged theses

Last update: 27/01/2023 05:30:20.

List of defended theses by year

No hi ha registres per mostrar.

Last update: 27/01/2023 06:00:13.

Research groups

• ACES-Advanced Control of Energy Systems
• ALBCOM-Algorithms, Computational Biology, Complexity and Formal Methods
• CoDAlab-Control, Dynamics and Applications
• COMBGRAPH-Combinatorics, Graph Theory and Applications
• DAMA-UPC-Data Management Group
• DCG-Discrete and Combinatorial Geometry
• gAGE-Research Group of Astronomy and Geomatics
• GEOMVAP-Geometry of Manifolds and Applications
• GIES-Geophysics and Earthquake Engineering
• GNOM-Mathematical Optimization Group
• GRAA-Research Group in Applied Analysis
• GREC-Knowledge Engineering Research Group
• GRHCT-Group of Research on History of Science and Technology
• GRTJ-Game Theory Research Group
• INSIDE-Innovation in Systems for Engineering Design and Training
• KEMLG-Knowledge Engineering and Machine Learning Group
• L'AIRE-Laboratory of Aeronautical and Industrial Research and Studies
• LACAN - UPC-Numerical Methods for Applied Sciences and Engineering
• LARCA-Laboratory of Relational Algorithmics, Complexity and Learnability
• MAK-Mathematics Applied to Cryptography
• MAPTHE-Matrix Analysis and Discrete Potential Theory
• SAC-Advanced Control Systems
• SARTI-MAR-Sistemes d'Adquisicio Remota de dades i Tractament de la Informacio en el Medi Mari
• TN-Number Theory Research Group
• VIS-Artificial Vision and Intelligent Systems

Teachers

• Alberich Carramiñana, Maria
• Alvarez Montaner, Josep
• Amoros Torrent, Jaume
• Arias Vicente, Irene
• Arroyo Balaguer, Marino
• Balbuena Martinez, M.Camino
• Baldoma Barraca, Inmaculada
• Barja Yañez, Miguel Angel
• Batlle Arnau, Carles
• Burillo Puig, Pep
• Cabre Vilagut, Xavier
• Carmona Mejias, Angeles
• Casanellas Rius, Marta
• Comellas Padro, Francesc de Paula
• Delshams i Valdes, Amadeu
• Diez Mejia, Pedro
• Encinas Bachiller, Andres Marcos
• Fabrega Canudas, Josep
• Farre Cirera, Rafel
• Fernandez Mendez, Sonia
• Fernandez Sanchez, Jesus
• Ferrer Biosca, Alberto
• Ferrer Llop, Josep
• Fiol Mora, Miguel Angel
• Franch Bullich, Jaume
• Freixas Bosch, Josep
• Garcia Planas, Maria Isabel
• Gargallo Peiró, Abel
• Giacomini, Matteo
• Gimenez Pradales, Jose Miguel
• Gracia Sabate, Xavier
• Guardia Munarriz, Marcel
• Guillamon Grabolosa, Antoni
• Herranz Sotoca, Javier
• Huerta Cerezuela, Antonio
• Huguet Casades, Gemma
• Lario Loyo, Joan C.
• Lazaro Ochoa, Jose Tomas
• Magret Planas, M. Dolors
• Martí Farré, Jaume
• Martin de la Torre, Pau
• Martinez-Seara Alonso, Maria Teresa
• Masdemont Soler, Josep Joaquim
• Miranda Galceran, Eva
• Mitjana Riera, Margarida
• Molina Blanco, Santiago
• Mora Gine, Mercè
• Morillo Bosch, Maria Paz
• Muñoz Lecanda, Miguel Carlos
• Muñoz Romero, Jose Javier
• Myers, Timothy
• Noy Serrano, Marc
• Olle Torner, Maria Mercedes
• Palacios Quiñonero, Francisco
• Pascual Gainza, Pere
• Pozo Montero, Francesc
• Puente del Campo, Maria Albina
• Quer Bosor, Jordi
• Ramirez Ros, Rafael
• Rio Doval, Anna
• Rodellar Benede, Jose
• Rodriguez Ferran, Antonio
• Roman Roy, Narciso
• Rotger Cerdà, Victor
• Rubio Massegu, Josep
• Rue Perna, Juan Jose
• Saez Viñas, Pablo
• Sainz Sapera, Luis
• Sanchez Soler, Mónica
• Sarrate Ramos, Jose
• Serra Albo, Oriol
• Silveira Isoba, Rodrigo Ignacio
• Sola-Morales Rubio, Joan
• Soler Villanueva, Jaume
• Susin Sanchez, Antonio
• Vazquez, Mariano
• Ventura Capell, Enric
• Vidal Segui, Yolanda
• Villar Santos, Jorge Luis