2020/2021
Research Seminar "Combinatorics of Vassiliev Invariants 2"
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Category 'Best Course for New Knowledge and Skills'
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
3, 4 module
Language:
English
ECTS credits:
3
Contact hours:
36
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 integrable hierarchies, tau-functions, generating series for polynomial invariants and connections between this objects
- Familiarity with the concept of categorification. Familiarity with the categorification of a Kaufmann bracket.
Assessment Elements
- The mark depends on the seminar attendance and the quality of the given talk.
- No final exam, the final mark is based on the regular seminar activity.
Interim Assessment
- Interim assessment (4 module)0.3 * No final exam, the final mark is based on the regular seminar activity. + 0.7 * The mark depends on the seminar attendance and the quality of the given talk.
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