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)

Notes：

knot_theory_Lecture1.pdf Lecture1_exercises.pdf knot_theory_Lecture2.pdf Exercises.pdf Trotter.pdf Lecture3FinalVersion.pdf Lecture4FinalVersion.pdf knot_theory_Lecture5.pdf

**About speaker:**

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

Education:

• 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.

Positions:

• 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)**

报名链接：https://www.wjx.top/vj/OFwax5v.aspx

课程微信群：

Course videos：

Lecture1(May12):

Lecture2(May15):

Lecture3(May19):

Lecture4(May26):