Lectures "Invariants and pictures"
-- V.O. Manturov
This lecture is given bilingually -- in English and in Russian
Lecture: 18:35 -- 20:00 (GMT+3) on Friday
Zoom link: 569 915 0694
Passcode: 901764
Seminar: 18:35 -- 20:00 (GMT+3) on Wednesday
Zoom link: 780 361 3594
Passcode: 141592
Lectures on Knot theory in Chinese
-- V.O. Manturov
Lecture: 15:00 -- 16:30 (GMT+8) on Sunday
Tencent link: 486 4356 1964
Passcode: 179325
Lectures on Knot theory
-- V.O. Manturov, S. Kim (
Lecture: 09:00 -- 10:25 (GMT+3) on Friday
Zoom link: 569 915 0694
Passcode: 901764
Seminar: 10:45 -- 12:10 (GMT+3) on Friday
Zoom link: 780 361 3594
Passcode: 141592
Лекции
"Теория узлов" и "Инварианты и картинки"
Уважаемые студенты,
Занятие Теория узлов, 4-мерная геометрия и топология, Группа 2021-2022 (Мантуров Василий Олегович) состоится по вторникам 17:05 - 20:00.
Войти в него можно по ссылке:
https://zoom.us/j/94529063258?pwd=MVIvMHQ3Sm9ZbHRpZkk4TnpnSWlUdz09
До встречи!
Knot Theory in Jilin university
Prof. V.O. Manturov will give lectures on knot theory
from 06/01/2021 at 13:00 (GMT+3), 18:00 (GMT+8) (in Chinese).
Lecture 1. Reidemeister moves. Colouring invariants, the linking number
报告时间:2022/01/06 18:00-19:00
Lecture 2. The Kauffman bracket, the Jones polynomial.
报告时间:2022/01/09 18:00-19:00
Lecture 3. Fundamental group. The knot group.
报告时间:2022/01/13 18:00-19:00
Lecture 4. The knot Quandle is a complete knot invariant.
报告时间:2022/01/16 18:00-19:00
Lecture 5. The braid groups
报告时间:2022/01/20 18:00-19:00
Lecture 6. The Alexander polynomial.
报告时间:2022/01/23 18:00-19:00
Lecture 7. Vassiliev invariant
报告时间:2022/01/27 18:00-19:00
Lecture 8. Khovanov homology
报告时间:2022/01/30 18:00-19:00
Zoom:
Meeting ID : 818 3620 2175
Lectures
"Knot theory" and "Invariants and pictures"
Dear colleagues,
On Tuesday, online lectures on "Knot theory" and "Invariants and pictures" are given by professor V.O. Manturov.
-
Теория узлов. Дополнительные главы / Knot Theory. Additional Chapters, Tuesday at 17:05 in Moscow
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Инварианты и картинки / Invariants and Pictures, вторник Tuesday at 18:35 in Moscow
Webpage: https://mipt.ru/education/chairs/dm/staff/manturov-vasiliy-olegovich-spetskursy.php
Zoom: https://zoom.us/j/94529063258?pwd=MVIvMHQ3Sm9ZbHRpZkk4TnpnSWlUdz09
Lectures "Knot theory" in Tsinghua university
Thursday & Sunday 15:20-16:55, May 12-July 7,2022
Speaker:Prof. Vassily Olegovich Manturov (Russian Academy of Sciences)
Venue:Zoom Meeting ID: 276 366 7254 Passcode: YMSC
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
Satellite conference of ICM2022
"Knot theory and Applications"
June 29 – July 4, 2022
A satellite conference of ICM2022 Knot theory and Applications will be held on June 29 – July 5, 2022 online as a fully virtual event.
Webpage: http://knots2022.rmc.math.tsu.ru/#rec308492594
Zoom: https://zoom.us/j/93407314006?pwd=dkdHeFlnZk1sbHRxNkdBZWNJaXdxUT09
Prof. V.O. Manturov will give
lectures on 4-dimensional geometry and topology
from 08/01/2022 at 14:00 (GMT+3), 19:00 (GMT+8) (in English).
ZOOM ID: 810 4009 0103,PW: 989134
Link: https://us02web.zoom.us/j/81040090103?pwd=OTVwM1BBN29Wb1gyL1JrVW40SFg0QT09
Lecture 1. 2023.01.08
The Poincare conjecture h-cobordism theorem
We formulate and proof the famous h-cobordism theorem by Smale
and the Poincare conjecture in dimensions greater than or equal to 5
Lecture 2. 2023.01.13
Freedman's proof of the Poincare conjecture in dimension 4.
We introduce Casson's handles and prove the topological Poincare
conjecture in dimension 4.
Lecture 3. 2023.01.15
Intersection forms.
We discuss algebraic classification of Z-valued quadratic forms.
We shall consider simply connected 4-manifolds and formulate
some classification results based on the intersection pairings on
second homology groups.
Lecture 4. 2023.01.20
Theorems of Wall and Rokhlin
We prove classical theorems of Wall (about stable equivalence of manifolds) and Rokhlin (about signatures and cobordidsms)
Lecture 5. 2023.01.27
Preliminary materials: spin structures, Clifford algebras
We introduce necessary algebraic background needed for formulation
of Donaldson and Seiberg-Witten invariants
Lecture 6. 2023.01.29
Donaldson's theorem
We sketch the proof of Donaldson's theorem that if an intersection
form of a smooth manifold is positive-definite then it is diagonalisable.
Lecture 7. 2023.02.03
Seiberg-Witten invariants
We give a quick introduction into Seiberg-Witten invariants and list results: short proof of Donaldson's theorem, triviality of SW results for positive curvature, exotic smooth structures
Lecture 8. 2023.02.05
Exotic R^{4}.
We discuss the approaches to constructing smooth structures on R^{4}
due to Freedman, Gompf, Taubes, including the celebrated Taubes'
theorem on continuously many different smooth structures