Knot Theory

Speaker:Prof. Vassily Olegovich Manturov (Russian Academy of Sciences)
Schedule:Thurdays & Sundays,15:20-16:55, May 12-July 7,2022;+(exercises)Sun.17:30-18:30,May15,May29,June12,June26;(no lecture on May22)updated
Venue:Zoom Meeting ID: 276 366 7254 Passcode: YMSC

Note: Lecture on May 22 is  cancelled.

Course schedule:

Lecture 1. Reidemeister moves, colouring invariants, linking number

Lecture 2. The Kauffman bracket and the Jones polynomial

Lecture 3. Fundamental group. The knot group

Lecture 4. The knot quandle. The complete knot invariant

Lecture 5. The braid group and the braid recognition algoritm

Lecture 6. Alexander's theorem and Markov's theorem

Lecture 7. The Alexander polynomial

Lecture 8. Quadrisecants of knots

Lecture 9. Vassiliev's invariants. The chord diagram algebra

Lecture 10. The Kontsevich integral

Lecture 11. The Khovanov homology

Lecture 12. The Rasmussen invariant. Sliceness obstructions

Lecture 13. Introduction to virtual knot theory

Lecture 14. The Khovanov homology for virtual knots with arbitrary coefficients

Lecture 15. Free knots and the parity bracket

Lecture 16. A survey of unsolved problems

(+Exercises: Sun.17:30-18:30, May15,May29,June12,June26)


knot_theory_Lecture1.pdf   Lecture1_exercises.pdf   knot_theory_Lecture2.pdf   Exercises.pdf   Trotter.pdf   Lecture3FinalVersion.pdf Lecture4FinalVersion.pdf   knot_theory_Lecture5.pdf   Lec 6.pdf   Lecture_6__Problems.pdf   Lecture_6__Exercises.pdf   Bigelow2000_Does the Jones Polynomial Detect the unknot.pdf    Jones1987_Hecke Algebra Representations of Braid Groups and Link Polynomial.pdf   Virtual Knots_The State of the Art.pdf    Lecture_7__Problems.pdf knot_theory_Lecture7.pdf   Lecture_7__Exercises.pdf  KileMiller2020 - alexander_polynomial.pdf   Denne2005 - Alternating Quadrisecants of Knots.pdf   Kuperberg2002 - Quadrisecants of knots and links.pdf   Lecture 8.pdf BarNatan1995 ON THE VASSILIEV KNOT INVARIANTS.pdf   Lecture_9‘’‘’.pdf   Sunday_Exercises.pdf   Lec 10.pdf   Lec 11.pdf    KhovanovHopfLink.pdf     Lec 13 final version.pdf   Virtual+Knots.+The+State+of+the+Art.pdf   FenKauffmanManturov - Virtual Knot Theory - Unsolved Problems.pdf   Lec_14B.pdf   Virtual+Knots.+The+State+of+the+Art.pdf  KauffmanDyeKaestner2022 (revised).pdf   Rush 2016 - ON THE VIRTUAL RASMUSSEN INVARIANT.pdf   Vassily_O_Manturov_2007_Izv._Math._71_967.pdf   Knot+Theory.+Second+Edition.pdf

About speaker:

Vassily Olegovich Manturov, Professor of Moscow Institute of Physics and Technology


• 2008, Habilitation Thesis "Geometry and Combinatorics of Virtual Knots”, M.V. Lomonosov Moscow State University

• 2002, Ph.D. "Bracket Structures in Knot Theory", M.V. Lomonosov Moscow State University

1995-2000, Student, Department of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Graduated with Excellence in Mathematics.


• Professor of RAS (elected in 2016),

• Managing Editor of the "Journal of Knot Theory and Its Ramifications”, since 2016,

• Bauman Moscow State Technical University, Full Professor, since November 2010,

• Editor-in-Chief's Deputy for "Proceedings of the Seminar on Vector analysis with its applications to geometry, mechanics, and physics", Moscow State University, in Russian (Proceedings are published since 1930s),

• Member of the Editorial Board of “ISRN Geometry”,

• Member of the Laboratory “Quantum Topology”, Chelyabinsk State University, Chelyabinsk, Russia,

• Member of the Moscow Mathematical Society, Member of the American Mathematical Society,

• Member of the dissertation council of the Kazan State University since 2019.

Note: Please register through the following link. (Deadline: April 28, 2022)



Course videos: