Master's & PhD

Ph.D. in Mathematical Modelling

Course duration
4 years
Applications period
18/09 to 01/12/2023


The Doctorate in Mathematical Modeling provides cutting-edge academic training, aligned with the needs of modern society, in all applications of mathematics for the solution of concrete problems. In addition, it trains professionals with specific skills in the various areas of mathematics and its applications, the field of scientific research that represents the distinguishing feature of the program.


To enable the doctoral student to analyze scenarios and support decision making in situations of intensive use of data and information, in addition to the objective of training excellent researchers in the area.


Masters in mathematics, statistics, applied mathematics, computing, engineering, physics, economics and related fields, who wish to work with academic, scientific and technological research in public or private institutions, supporting the decision-making process in any spheres.

About the course

Research lines

This line of research began worldwide with the development of Probability and the formal construction of the Brownian Movement in the early 20th century. This is probably one of the areas of mathematics with the most applications in the real world. From a theoretical point of view, we are interested in the study of Stochastic Differential Equations and the incorporation of path-dependence in several aspects of the theory.

In addition, another aspect of this line is the numerical resolution of differential equations, in particular random (RDEs) and stochastic (EDEs). The theory of EDEs and RDEs are themes, at the crossroads of differential equations and stochastic processes, with a wide variety of applications in the modeling of phenomena and practical situations in which the quantities of interest are subject to random disturbances. Since obtaining solutions to these equations is rarely possible, much attention is paid to the construction and study of approximation methods, with good qualitative properties, for their integration and simulation.

The Optimal Control Theory studies Optimization problems whose state variables are subject to differential equations (ordinary or partial) whose dynamics depend on a control variable, while Stochastic Optimization is focused on the study of optimization problems involving uncertainties modeled by a stochastic process. A stochastic optimization problem is usually formulated using conditional risk measures.

In this line of research, mathematical models and methods are studied with a focus on applications in problems of Finance, Economics and Actuarial Sciences. For applications in Finance and Economics, research projects are usually based on techniques involving Stochastic Calculation and/or Partial Differential Equations, whereas applications in Actuarial Sciences, such as Reserves calculation, tend to use statistical regression models or time series.

Mathematical epidemiology is an applied mathematics subject with more than a century of tradition, which incorporates ideas and methods from different branches of mathematics in the representation and analysis of its objects of study.   
At EMAp, the Mathematical Epidemiology group studies how information on how communicable diseases can be treated from a quantitative point of view, differently from the classic statistical techniques well known in the medical field. In addition, the projects require a basic understanding of biological assumptions and the mathematical models that underlie infection models and the tools available today to extract biological information from these models.

In general, this line of research is divided into theoretical, methodological and applied aspects involving data analysis. In particular, EMAp researchers are interested in the following areas of Statistics: Estimation of time series in high dimension; Modeling of non-linear time series; Non-parametric tests; Monte Carlo simulation for Bayesian inference; Statistical inference for stochastic optimization problems averse to risk or neutral risk (central limit theorems, hypothesis tests, non-asymptotic confidence intervals); Nonparametric hypothesis testing using convex optimization techniques.

The objective of this line of research is the exploration and development of objects and research problems through methods originated from the statistical learning of machines (Machine Learning) and its applications in the analysis of structured and unstructured data. This range of empirical objects encompasses numerical, categorical and textual data, images, graphs, time series, among others. It also includes the development of algorithms, languages and methodologies for manipulating these complex databases, in tasks such as classification, regression, learning, identification of clusters, recommendation systems, optimization, extraction and representation of knowledge, modeling knowledge domains, data mining, text mining, visualization, sentiment analysis, high-dimensional data analysis, cryptography.

FGV Main Office

Praia de Botafogo, 190 Rio de Janeiro - RJ. Zip Code: 22250-900 Tel: +55 21 3799-5917 E-mail:

Ombudsman FGV

Ph.D. in Mathematical Modelling

Curriculum Grid

The PhD in Mathematical Modeling at FGV EMAp has as its disciplinary axes the Applied and Computational Mathematics, and Data Science.

To obtain a Doctoral degree, the student must earn a minimum of 33 credits, distributed as follows: one for approval of the Thesis; four obtained through participation in Research Seminars; and a minimum of 28 credits, corresponding to the approval of three core courses totaling 12 credits, and four elective courses totaling 16 credits. The elective courses must belong to two distinct research lines.


In the application form, candidates must enter their personal and academic data, as detailed in the respective notice.

Registration will be formalized by uploading the documentation below, on the Selection Process registration page, available on the School page. The following documents must also be sent:

  1. ID;
  2. Passport (foreign applicants);
  3. Lattes / CNPq Curriculum ( attaching copies of the most relevant works, when available (optional) or Curriculum Vitae;
  4. Letter of Intent (required);
  5. Research Proposal (required);
  6. Letter of recommendation (optional);
  7. Medical Report (People with Disabilities) - item 9.2.5 e annex III;
  8. Undergraduate degree. In the case of a course taken abroad, the document must be consularized by the Brazilian representative at the Embassie/Consulates in the country of origin of the Diploma or apostilled, according to the Haia Convention, and presented with a sworn translation;
  9. Candidates in the process of completing their Undergraduate course may submit, for registration to the Selection Process, a statement with the expected completion of the course (issued less than 60 days ago). For the effective enrollment, it will be mandatory to present the Diploma or Declaration containing the date of graduation;
  10. Certificate of completion of postgraduate courses (optional).


  1. Documents must be scanned, saved in "PDF" format and attached to the Registration Form;
  2. Photos of documents will not be accepted;
  3. The maximum size allowed for uploading each document is 1.5MB;
  4. Documents that have front and back or more than 1 (one) page, must be scanned in a single file (ID, passport, Diploma etc);
  5. Candidates should consult the status of the documentation sent through the website, in the Overview menu, in the link Follow-up your Registration. Documents will be verified within 3 (three) business days after confirmation of payment of the registration fee.


The selection process will be directed by the Graduate Program Coordination and will consist of 2 (two) stages, which are eliminatory in nature:

  • 1st stage - Document analysis and analysis of the Curriculum Vitae or Lattes;
  • 2nd stage - Candidates approved in the 1st stage will be called for an interview.


There may be approved candidates who are not ranked due to the number of available slots. Approved but not ranked candidates will be arranged in descending order and will form a waiting list that may lead to enrollment in case of withdrawal or disqualification of ranked candidates.

In case of a tie, the classification will be defined based on the following criteria:

  1. Higher grade in document analysis and curriculum;
  2. Higher grade in leveling subjects, for designated candidates;
  3. If the tie persists, the age criterion will be used, with the oldest student being selected.


The list of approved candidates and the waiting list will be published, according to the schedule (Annex I), on FGV EMAp’s website ( after the completion of the stages described in the notice.




  • Coming soon


To review the documents and procedures necessary for enrollment, the candidate should follow the detailed instructions in the mentioned notice, section 9 - Enrollment.


The cancellation of enrollment must be made by the contracting party, via a request filed with the SRA - Secretariat for Academic Records. For billing Legal Entities, consult our financial services at the Academic Records Secretariat - SRA.

Additional Information


Praia de Botafogo, 190 - CEP 22250-900, Rio de Janeiro, RJ


Praia de Botafogo, 190, 5th floor - CEP 22250-900, Rio de Janeiro, RJ

Phone: (21) 3799-5917


Office Hours: Monday to Friday, from 8 am to 5 pm


A / C: Selection Process for the Masters in Mathematical Modeling

Praia de Botafogo, 190 / office 314 - 3rd floor

Zip code 22250-900, Rio de Janeiro, RJ

Phone: (21) 3799-5757


Office Hours: 9 am to 6 pm

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