2021/2022
Research Seminar "Combinatorics of Vassiliev Invariants 2"
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
Open to:
students of all HSE University campuses
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 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
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
- 2021/2022 4th module0.7 * The mark depends on the seminar attendance and the quality of the given talk. + 0.3 * No final exam, the final mark is based on the regular seminar activity.
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