Doctoral Studies

Geometry, Topology and Global Analysis - Field

Brief description of 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

Profile of  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

Requirements for applicants
The knowledge at the level of master’s state exam in mathematics. In particular, the applicant has to be well familiar with the courses in linear algebra, mathematical analysis, topology
and differential geometry.
Knowledge of the English language.
The applicant has elected advisor and subject of dissertation.

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
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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