Research 4

2022/2023
Programme:
Doctoral Programme Mathematics and Physics
Orientation:
Mathematics
Year:
4 year
Semester:
first and second
Kind:
mandatory
ECTS:
54
Language:
slovenian, english
Hours per week – 1. semester:
Lectures
0
Seminar
0
Tutorial
0
Lab
0
Hours per week – 2. semester:
Lectures
0
Seminar
0
Tutorial
0
Lab
0
Content (Syllabus outline)

The student starts his research on the main topic of PhD studies. He studies the relevant literature in detail. He considers several approaches to the solution of the proposed problem and states basic conjectures. In order to obtain as general a solution of the problem as possible, he considers some special cases. Finally, he thoroughly prepares manuscripts involving solutions of the problem and submits them for evaluation to relevant international journals. Within the course students can attend professional meetings.

Readings

Izbira temeljne literature je pomemben del raziskovalnega dela. Študent jo izbere sam z morebitnimi nasveti mentorja.

How to chose relevant literature is an important part of the research work. A student should be able to chose it alone with some possible suggestions of the supervisor.

Objectives and competences

The student solves a proposed problem of doctoral thesis and prepares a relevant manuscript.

Intended learning outcomes

After the course is completed, a student is able to continue a research either on the field of doctoral thesis or wider.

Learning and teaching methods

Individual study and consultations.

Assessment

Grades: pass, fail.

Lecturer's references

Franc Forstnerič:
FORSTNERIČ, Franc. Noncritical holomorphic functions on Stein spaces. Journal of the European Mathematical Society, ISSN 1435-9855, 2016, vol. 18, iss. 11, str. 2511-2543. [COBISS-SI-ID 17787481]
ANDRIST, Rafael, FORSTNERIČ, Franc, RITTER, Tyson, WOLD, Erlend Fornæss. Proper holomorphic embeddings into Stein manifolds with the density property. Journal d'analyse mathématique, ISSN 0021-7670, 2016, vol. 130, iss. 1, str. 135-150. [COBISS-SI-ID 17810265]
ALARCÓN, Antonio, FORSTNERIČ, Franc, LÓPEZ, Francisco J. Embedded minimal surfaces in R[sup]n. Mathematische Zeitschrift, ISSN 0025-5874, 2016, vol. 283, iss. 1, str. 1-24. [COBISS-SI-ID 17544025]

Primož Potočnik:
BERČIČ, Katja, POTOČNIK, Primož. Two-arc-transitive two-valent digraphs of certain orders. Ars mathematica contemporanea, ISSN 1855-3966. [Tiskana izd.], 2016, vol. 11, no. 1, str. 127-146. [COBISS-SI-ID 1538308036]
POTOČNIK, Primož, WILSON, Stephen. Linking rings structures and semisymmetric graphs: Cayley constructions. European journal of combinatorics, ISSN 0195-6698, 2016, vol. 51, str. 84-98. [COBISS-SI-ID 17462361]
POTOČNIK, Primož, SPIGA, Pablo, VERRET, Gabriel. Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs. Journal of combinatorial theory. Series B, ISSN 0095-8956, 2015, vol. 111, str. 148-180. [COBISS-SI-ID 1537132228]

Emil Žagar:
KOVAČ, Boštjan, ŽAGAR, Emil. Curvature approximation of circular arcs by low-degree parametric polynomials. Journal of numerical mathematics, ISSN 1570-2820, 2016, vol. 24, iss. 2, str. 95-104. [COBISS-SI-ID 17724505]
JAKLIČ, Gašper, KOZAK, Jernej, KRAJNC, Marjetka, VITRIH, Vito, ŽAGAR, Emil. High order parametric polynomial approximation of conic sections. Constructive approximation, ISSN 0176-4276, 2013, vol. 38, iss. 1, str. 1-18. [COBISS-SI-ID 16716121]
JAKLIČ, Gašper, KOZAK, Jernej, KRAJNC, Marjetka, VITRIH, Vito, ŽAGAR, Emil. Hermite geometric interpolation by rational Bézier spatial curves. SIAM journal on numerical analysis, ISSN 0036-1429, 2012, vol. 50, no. 5, str. 2695-2715. [COBISS-SI-ID 16449369]