Кандидат физ.-мат. наук

University

National Research Tomsk State University

Level of English proficiency

Educational program and field of the educational program for which the applicant will be accepted

01.04.01 Mathematics (educational program)

01.04.01 Mathematics (field of the educational program)

01.04.01 Mathematics (field of the educational program)

List of research projects of the potential supervisor (participation/leadership)

“Construction of conformal mappings of the half-plane onto

circular polygons" (RFBR, 2018-2019, lider)

“Development of geometric methods for estimating energy levels of quantum billiards” (RSF, 2023-2024, participation)

circular polygons" (RFBR, 2018-2019, lider)

“Development of geometric methods for estimating energy levels of quantum billiards” (RSF, 2023-2024, participation)

List of the topics offered for the prospective scientific research

List of 7-10 scientific topics, which are offered by the research supervisor for consideration of foreign applicants

– One-parameter method for constructing conformal mappings of domains of a special type

– Solving extremal problems of complex analysis using the variational method

– Finding the modulus of doubly connected and simply connected regions

– Conformal mapping of multiply connected regions

– Algorithm for constructing a conformal mapping for the MatLab mathematical package

– Parametric Levner method: control function generating a cut adjacent at zero angle to the boundary

– Generalization of the Christoffel-Schwartz formula for areas of a special type

– Construction of minimal surfaces using conformal mappings

(During the course of the Interview the topic may be modified according to specific area of scientific interest of the applicant)б

– One-parameter method for constructing conformal mappings of domains of a special type

– Solving extremal problems of complex analysis using the variational method

– Finding the modulus of doubly connected and simply connected regions

– Conformal mapping of multiply connected regions

– Algorithm for constructing a conformal mapping for the MatLab mathematical package

– Parametric Levner method: control function generating a cut adjacent at zero angle to the boundary

– Generalization of the Christoffel-Schwartz formula for areas of a special type

– Construction of minimal surfaces using conformal mappings

(During the course of the Interview the topic may be modified according to specific area of scientific interest of the applicant)б

Supervisor’s research interests

The research concerns the geometric theory of functions of a complex variable. Generalization of the Christoffel-Schwarz formula for regions of a special type. Development of a method for constructing conformal mappings of a canonical domain onto polygons with a rectilinear boundary, as well as polygons with a boundary consisting of circular arcs. The problem of determining the conformal modulus of a region. Variational and parametric Levner method for solving extremal problems of function theory.

Supervisor’s main publications

- Kolesnikov I.A.
*Interior Modulus of Polygonal Quadrilateral*// Lobachevskii Journal of Mathematics, 2023, Vol. 44, No. 4, pp. 1358–1364 - Борисова Я. В., Колесников И. А., Копанев С. А., Садритдинова Г.Д.
*Решение задачи Фекете и Сеге вариационным методом*// Дальневост. матем. журн., 2021, 21:2, C. 133–150 DOI: 10.47910/FEMJ202112 - Kolesnikov I.A. A one-parametric method for determining

DOI: 10.1134/S0037446621040078

- Kolesnikov I. A.
*Conformal mapping from the half-plane onto a circular polygon with cusps*// Russian Math. (Iz. VUZ), 2021, Vol. 65, No. 6 pp. 8–20

Supervisor’s specific requirements

Knowledge of basic mathematics courses, in particular complex analysis