Individual study 1

2022/2023
Programme:
Doctoral Programme Mathematics and Physics
Orientation:
Mathematics
Year:
1 year
Semester:
first and second
Kind:
mandatory
ECTS:
6
Language:
slovenian, english
Lecturer (contact person):

Znan. sod. dr. Gregor Kosec, Prof. Dr. Primož Potočnik

Hours per week – 1. semester:
Lectures
0
Seminar
0.33
Tutorial
0
Lab
0
Hours per week – 2. semester:
Lectures
0
Seminar
0
Tutorial
0
Lab
0
Content (Syllabus outline)

The student independendly learns a major topic from his specific research field. The topic and literature is determined by the mentor.

Readings

Študent literaturo izbere v sodelovanju s svojim mentorjem.

The literature is chosen in cooperation with the mentor.

Objectives and competences

The student learns a specific topic, needed for the in-depth research work in his or her research field.

Intended learning outcomes

Knowledge and understanding: The student will get acquainted with the key results in his specific research area on the level that facilitates their usage when tackling original research problems.

Application: The acquired knowledge and skills will be used in original research and proving new results.

Reflection: The acquired knowledge will be appropriately reflected.

Transferable skills: The skill of understanding deep mathematical arguments and the usage of classical results in original research work.

Learning and teaching methods

Individual study and consultations.

Assessment

Homework and oral exam. Grades: pass, fail.

Lecturer's references

Matej Brešar:
BREŠAR, Matej. Functional identities on tensor products of algebras. Journal of algebra, ISSN 0021-8693, 2016, vol. 455, str. 108-136. [COBISS-SI-ID 17625945]
BREŠAR, Matej. Algebras in which non-scalar elements have small centralizers. Linear and Multilinear Algebra, ISSN 0308-1087, 2015, vol. 63, no. 9, str. 1864-1871. [COBISS-SI-ID 17160537]
BREŠAR, Matej, ŠPENKO, Špela. Functional identities of one variable. Journal of algebra, ISSN 0021-8693, 2014, vol. 401, str. 234-244.[COBISS-SI-ID 16842329]

Alexander Simpson:
AWODEY, Steve, BUTZ, Carsten, SIMPSON, Alex, STREICHER, Thomas. Relating first-order set theories, toposes and categories of classes. Annals of pure and applied Logic, ISSN 0168-0072. [Print ed.], 2014, vol. 165, iss. 2, str. 428-502. [COBISS-SI-ID 17089881]
EGGER, Jeff, MØGELBERG, Rasmus Ejlers, SIMPSON, Alex. The enriched effect calculus: syntax and semantics. Journal of logic and computation, ISSN 0955-792X, 2014, vol. 24, iss. 3, str. 615-654. [COBISS-SI-ID 17090137]
SIMPSON, Alex. Measure, randomness and sublocales. Annals of pure and applied Logic, ISSN 0168-0072. [Print ed.], 2012, vol. 163, iss. 11, str. 1642-1659. [COBISS-SI-ID 17091161]

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]