## Doctorate in Science with Specialization in Mathematics

Degree: Doctorate in Science with Specialization in Mathematics

Duration: Four years

Schedule: From Monday to Friday between 8.30 and 18.30, clases daytime, fulltime, face-to-face and blended teaching

ObjectivesThe objective of the Program is to form Doctors in Science specialized in Mathematics with broad knowledge of the discipline and the capability to conduct research indepentently.

The specific objectives of the Program are:

1. Contribute to regional and national development through the training of people with high levels of excellence, capable of creating new knowledge in the area of mathematics, with competences to produce scientific innovations appropriate to the requirements demanded by Chile.

2. To train highly qualified human resources capable of cooperating in university research and teaching in the field of mathematics.

3. Deliver advanced mathematics training to teachers and students from other countries in the region.

Graduate profile

The graduate of the Ph.D. program in Mathematics has knowledge, skills and abilities to formulate and autonomously carry out leading research in Mathematics, in order to contribute to regional, national and international development in the area of his/her specialization.

Areas of researchConsidering the experience of the Department of Mathematics and Statistics of the University of La Frontera in the teaching aspects of undergraduate and postgraduate studies, in addition to the degree of development and level of preparation the Academic staff, and the present physical and technological infrastructure, the following have been defined as areas of development and lines of research for the Program:

1.- Algebra and geometry

2.- Analysis

The respective lines and researchers of which are detailed below:

1. Algebra y Geometry:

Researchers (UFRO): Ángel Carocca, Carolina Canales, Ana Cecilia de la Maza, Mauricio Godoy, Rubén Hidalgo, Saúl Quispe, Sebastián Reyes, Rubí Rodríguez.

Collaborating researchers: Anita Rojas (UChile), Michela Artebani (UdeC), Antonio Laface (UdeC), Víctor González (UTFSM), Mariela Carvacho (UTFSM)

Lines of research: Algebraic Geometry, Riemann Surfaces, Kleinian Groups, Abelian Varieties, Moduli and Definition Bodies, Differential Geometry, Geometric Control Theory, Number Theory

2. Analysis:

Researchers (UFRO): Andrés Ávila, Mario Choquehuanca, Erwin Henríquez, Elena Olivos, Alex Sepúlveda, Herme Soto.

Collaborating researchers: Claudio Cuevas (UFP), Herminia Ochsenius (PUC).

Lines of research: Partial Differential Equations, Numerical Methods, Evolution Equations, Non-Archimedean Analysis.

Admission requirements

According to Article no. 6 of the Program Regulations, to apply for admission to the Doctorate Program, the applicant must:

1. Have the Higher Degree or Master’s degree or an equivalent degree in level and orientation, in the area of Mathematical Sciences, and that assures a previous training satisfactory for the aims of the program.

2. Submit two letters of recommendation, at least one of which must be from an academic from the University where she/he graduated or from the University or Institution where she/he currently works.

3. Submit a letter of motivation, indicating at least the candidate's field of interest, possible advanced work, and eventual dedication to the Program.

4. To present in the secretariat of the postgraduate program the complete antecedents in the official forms and within the deadlines established in the annual convocation that realizes the Academic Direction of Postgraduate of the University of Frontera.

Selection system

According to Article no. 7 of the Program Regulations, the process of selecting applicants follows the following procedure:

1. The Program Director will send applications for admission to the Academic Committee of the Program, informing of the deadlines for the entire selection process.

2 . The Academic Committee of the Program will propose the acceptance or rejection of the applicant on the basis of his academic background, letters of recommendation and any advanced work presented, with the following consideration:

2.1.- Academic background of the applicant (50% of the total)

2.2.- Professional / academic career of the applicant. (40% of the total)

2.3.- Study Objectives - Letter of motivation (Research line – Tutoring professor). (10% of the total)

3.- In addition, the Academic Committee may require a personal interview and / or admission examination, if deemed necessary. In this case, with the following consideration:

3.1.- Academic background of the applicant- Professional / academic career of the applicant – Study objectives – Letter of motivation (Research line – Tutoring professor). (70% of the total)

3.2.- Personal interview and/or admission exam. (30% of the total)

4.- The Program Director will notify the acceptance or rejection of the applications for admission in accordance with the proposals of the Academic Committee.

Structure of the Program and description of studies

The curricular structure of the program consists of three training cycles.

First cycle Second cycle Third cycle

FIRST YEAR SECOND YEAR THIRD YEAR FOURTH YEAR

Obligatory I

Advanced linear algebra Obligatory II

Topology Optional First level Optional Second level Optional Second level Elaboration Thesis I Optional Second level

Elaboration Thesis III

(15 sct) (15 sct) (15 sct) (15 sct) (15 sct) (15 sct) (15 sct) (15 sct)

Obligatory II

Analysis I Obligatory IV

Abstract Algebra I Optional First level Research Seminar Research Seminar Elaboration Thesis II Research Seminar Elaboration Thesis IV

(15 sct) (15 sct) (15 sct) (15 sct) (15 sct) (15 sct) (15 sct) (15 sct)

SUBJECTSAdvanced Linear Algebra

Analysis I

Topology

Abstract Algebra I

Optional First Level

Optional First Level

Optional Second Level

Research Seminar

Elaboration Thesis I

Optional Second Level

Elaboration Thesis II

Research Seminar

Elaboration Thesis III

Optional Second Level

Elaboration Thesis IV

Research Seminar