Master
2024/2025
Research Seminar "Combinatorics of Invariants 2"
Type:
Elective course (Mathematics)
Area of studies:
Mathematics
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
2 year, 3, 4 module
Mode of studies:
offline
Open to:
students of all HSE University campuses
Master’s programme:
Mathematics
Language:
English
ECTS credits:
3
Course Syllabus
Abstract
This students' research seminar is devoted to combinatorial problems arising in knot theory. The topics include finite order knot invariants, graph invariants, matroids, delta-matroids, integrable systems and their combinatorial solutions. Hopf algebras of various combinatorial species are studied. Seminar's participants give talks following resent research papers in the area and explaining results of their own.
Learning Objectives
- To introduce the subject area to the students, and to offer them an opportunity to prepare and give a talk, as well as to start research on their own.
Expected Learning Outcomes
- Familiarity with the concept of categorification. Familiarity with the categorification of a Kaufmann bracket.
- Familiarity with the concept of integrable hierarchies, tau-functions, generating series for polynomial invariants and connections between this objects
Interim Assessment
- 2024/2025 4th moduleRegular participation in the seminar is necessary for marking. However, the participation only can not contribute more than 8 points. For getting a higher score, you have to give a talk either on resent actual papers or on your own results in scientific directions of the seminar.
Bibliography
Recommended Core Bibliography
- Chmutov, S., Duzhin, S., & Mostovoy, J. (2011). Introduction to Vassiliev Knot Invariants. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1103.5628
Recommended Additional Bibliography
- Bar-Natan, D., & Burgos-Soto, H. (2013). Khovanov homology for alternating tangles. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1305.1695
- Kazarian, M., & Lando, S. (2015). Combinatorial solutions to integrable hierarchies. https://doi.org/10.1070/RM2015v070n03ABEH004952