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Обычная версия сайта
2020/2021

Научно-исследовательский семинар "Комбинаторика инвариантов Васильева 2"

Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Лучший по критерию «Новизна полученных знаний»
Статус: Дисциплина общефакультетского пула
Когда читается: 3, 4 модуль
Язык: английский
Кредиты: 3
Контактные часы: 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

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

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.
Course Contents

Course Contents

  • Combinatorial solutions to integrable hierarchies
  • Khovanov homology
Assessment Elements

Assessment Elements

  • non-blocking The mark depends on the seminar attendance and the quality of the given talk.
  • non-blocking No final exam, the final mark is based on the regular seminar activity.
Interim Assessment

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

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