In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose K is a knot given in the form of a knot diagram. Consider a disc D in the projection plane of the diagram whose boundary circle intersects K exactly four times. We may suppose that (after planar isotopy) the disc is geometrically round and the four points of intersection on its boundary with K are equally spaced. The part of the knot inside the disc is a tangle. There are two reflections that switch pairs of endpoints of the tangle. There is also a rotation that results from composition of the reflections. A mutation replaces the original tangle by a tangle given by any of these operations. The result will always be a knot and is called a mutant of K. Mutants can be difficult to distinguish as they have a number of the same invariants. They have the same hyperbolic volume (by a result of Ruberman), and have the same HOMFLY polynomials. (Wikipedia).
Algebraic topology: Fundamental group of a knot
This lecture is part of an online course on algebraic topology. We calculate the fundamental group of (the complement of) a knot, and give a couple of examples. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52yxQGxQoxwOtjIEtxE2BWx
From playlist Algebraic topology
Introduction to Algebraic Theory of Quandles (Lecture - 2) by Valeriy Bardakov
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
Introduction to Algebraic Theory of Quandles (Lecture - 1) by Valeriy Bardakov
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
MegaFavNumbers - 1701936 knots
My contribution to the #MegaFavNumbers project. A brief introduction to mathematical knot theory, and a 19th-century Theory of Everything that didn't quite work out. References: J Hoste, M Thistlethwaite, J Weeks, "The First 1701936 Knots", Mathematical Intelligencer 20.4 (1998) 33-48
From playlist MegaFavNumbers
Knot polynomials from Chern-Simons field theory and their string theoretic... by P. Ramadevi
Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries
From playlist Quantum Fields, Geometry and Representation Theory
Polynomial Invariants of Virtual Knots by Andrei Vesnin
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
Does Our Reality Actually Exist? | Exploring The World Of Quantum Physics (Part 2 of 2) | Spark
Professor Jim Al-Khalili traces the story of arguably the most important, accurate and yet perplexing scientific theory ever: quantum physics. The story of quantum physics starts at the beginning of the 20th century with scientists trying to better understand how light bulbs work. This si
From playlist Happy Birthday Professor Jim Al-Khalili!
Three Knot-Theoretic Perspectives on Algebra - Zsuzsanna Dancso
Zsuzsanna Dancso University of Toronto; Institute for Advanced Study September 21, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Mind-Blowing Facts About Our Reality [4K] | The Secrets of Quantum Physics | Spark
Professor Jim Al-Khalili traces the story of arguably the most important, accurate and yet perplexing scientific theory ever: quantum physics. The story of quantum physics starts at the beginning of the 20th century with scientists trying to better understand how light bulbs work. This si
From playlist Happy Birthday Professor Jim Al-Khalili!
What's a knot? Geometry Terms and Definitions
A mathematical definition of a knot. Geometer: Louise McCartney Artwork: Kelly Vivanco Director: Michael Harrison Written & Produced by Kimberly Hatch Harrison and Michael Harrison ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www.patreon.com/socratica ► Mak
From playlist Socratica: The Geometry Glossary Series
Knots and surfaces I | Algebraic Topology | NJ Wildberger
This lecture is an introduction to knot theory. We discuss the origins of the subject, show a few simple knots, talk about the Reidemeister moves, and then some basic invariants, namely minimal crossing number, linking number (for links) and then the Alexander-Conway polynomial. This is p
From playlist Algebraic Topology
Untangling the beautiful math of KNOTS
Visit ► https://brilliant.org/TreforBazett/ to help you learn STEM topics for free, and the first 200 people will get 20% off an annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor Suppose yo
From playlist Cool Math Series
"Symmetrie und Ähnlichkeit" - Vortrag von Prof. Martin Grohe
Aufzeichnung des Vortrags "Symmetrie und Ähnlichkeit" von Prof. Dr. Martin Grohe (RWTH Aachen) im Rahmen der öffentlichen Reihe "Brücken in der Mathematik" an der WWU Münster. Darum geht es: Muster auf Schmetterlingsflügeln, Schneekristalle, Blütenblätter – symmetrische Strukturen sind in
From playlist Brücken in der Mathematik
Is the Conway knot slice? (After Lisa Piccirillo)
This is a talk on the recent work by Lisa Piccirillo showing that the Conway know is not a slice knot. We first review the definitions of the Conway know and slice knots, and then give an overview of her proof. The paper on this by Lisa Piccirillo can be found at https://arxiv.org/pdf/1
From playlist Math talks
Bourbaki - 05/11/2016 - 2/4 - Arnaud de MESMAY
Arnaud de MESMAY - Nœuds, mouvements de Reidemeister et algorithmes (d’après Lackenby) Un nœud est souvent représenté par un diagramme de nœud, c’est-à-dire une projection sur deux dimensions, où l’on indique à chaque croisement lequel des deux brins passe au-dessus de l’autre. Deux diagr
From playlist Bourbaki - 05 novembre 2016
Mathematics as Metaphor - Curtis McMullen (Harvard University)
Public lecture
From playlist Mathematics Research Center
Sergey Fomin: Morsifications and mutations
Abstract: I will discuss a connection between the topology of isolated singularities of plane curves and the mutation equivalence of the quivers associated with their morsifications. Joint work with Pavlo Pylyavskyy, Eugenii Shustin, and Dylan Thurston. Recording during the thematic meeti
From playlist Topology
A survey of quandle theory by Mohamed Elhamdadi
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onli
From playlist Knots Through Web (Online)