Магистратура
2024/2025
Научно-исследовательский семинар "Комбинаторика инвариантов 1"
Статус:
Курс по выбору (Математика)
Направление:
01.04.01. Математика
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
2-й курс, 1, 2 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для всех кампусов НИУ ВШЭ
Прогр. обучения:
Математика
Язык:
английский
Кредиты:
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 Lie algebras, the process of constructing weight systems from Lie algebras. Weight system of sl2
- Familiarity with the concept of weight systems and related topics
- Familiarity with the concepts of Hopf algebra and delta-matroids. Understanding the connection between chord diagrams, embedded graphs and delta-matroids
Course Contents
- Weight systems
- Constructing weight systems from Lie algebras
- Hopf algebra of graphs, chord diagramms and delta-matroids
Interim Assessment
- 2024/2025 2nd 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
- Kazarian, M., & Lando, S. (2015). Combinatorial solutions to integrable hierarchies. https://doi.org/10.1070/RM2015v070n03ABEH004952
- Moffatt, I. (2006). Knot invariants and the Bollobas-Riordan polynomial of embedded graphs. https://doi.org/10.1016/j.ejc.2006.12.004