Doctoral Studies

Geometry, Topology and Global Analysis - Field

Brief description of field

The doctoral studies program in this field  is oriented towards differential geometry, global analysis and algebraic topology. In accordance with the subject of dissertation, the student is individually oriented to work in one of these domains deeply. An important part of the doctoral study is individual research work.

 

Aims of the study

The principal aim is to write down the dissertation, that must contain original research results published in professional journals. So the student has to master such knowledge that enables him/her to  penetrate deeply  into the domain of dissertation and, at the same time, supplies him/her with broad look to differential and algebraic topology.

Profile of a typical graduate

The graduate has abilities of good orientation in the narrow domain of his specialization and of individual research work. The graduate is well prepared for the position of researcher in fundamentals research or a high school teacher.

Requirements for applicants

The applicant must succeed in the exam, which tests his/her orientation in Mathematics and ideas about the field  (max 50 points). It further tests the ability to study and present material in English  (max 30 points) and ideas of the applicant about the advisor and possibly the topic of the thesis (max 20 points). Minimum of 80 points is needed for acceptance. The entering exam may be organized also online using software support, or can be waived, based on documented proffesional experience of the applicant. The exact topic of the  thesis should be specified before the start of the second year of the study (including the choice of the advisor).

 

Study requirements and completion of studies

Individual study plan

In the course of doctoral studies, the student has to pass six one-semester courses prescribed for doctoral study.

In agreement with the advisor, the student aims his/her individual study to extending the knowledge in the scientific domain in question as well as to mastering the special subjects needed for his/her dissertation.

Student regularly participates scientific seminars.

Student assists in teaching undergraduates.

Study requirements and completion of studies

The subjects and the extend of the state doctoral exam, the required knowledge

Before submitting the application for the state doctoral exam, the student must satisfy all requirements set by the advisor.

On advisor’s proposal, the doctoral committee selects for the student three of the folowwing subjects.

  • Analysis on manifolds
  • Algebraic topology
  • Riemannian geometry
  • Differential geometry of fibered manifolds
  • Homological algebra
  • Applications of differential geometry in mathematical physics
  • Representations of Lie groups and algebras

The subjects and the extend of the state doctoral exam, the required knowledge

On advisor’s proposal, the doctoral committee selects for the student three of the folowwing subjects.

  • Analysis on manifolds
  • Algebraic topology
  • Riemannian geometry
  • Differential geometry of fibered manifolds
  • Homological algebra
  • Applications of differential geometry in mathematical physics
  • Representations of Lie groups and algebras

Requirements on the dissertation work

The dissertation work must contain original scientific results that are published or accepted for publication in scientific journals.

Domains of subjects of dissertations

  • Topology of homogeneous spaces
  • Geometric structures of mathematical physics
  • Differential geometric objects and operations
  • Strongly homotopic algebras
  • Geometric structures on manifolds
  • Topological conditions for existence of geometric structures
  • Geometry of multisymplectic structures

A List of current PhD theses topics for the academic year is found on the page below.

Individual study plan

In the course of doctoral studies, the student has to pass six one-semester courses prescribed for doctoral study.

In agreement with the advisor, the student aims his/her individual study to extending the knowledge in the scientific domain in question as well as to mastering the special subjects needed for his/her dissertation.

Student regularly participates scientific seminars.

Student assists in teaching undergraduates.

List of members of doctoral committee

List of supervisors

Commission for state doctoral exams and defenses

List of current doctoral topics

Department pages


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