In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, (in topology, a circle is not bound to the classical geometric concept, but to all of its homeomorphisms). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing through itself. Knots can be described in various ways. Using different description methods, there may be more than one description of the same knot. For example, a common method of describing a knot is a planar diagram called a knot diagram, in which any knot can be drawn in many different ways. Therefore, a fundamental problem in knot theory is determining when two descriptions represent the same knot. A complete algorithmic solution to this problem exists, which has unknown complexity. In practice, knots are often distinguished using a knot invariant, a "quantity" which is the same when computed from different descriptions of a knot. Important invariants include knot polynomials, knot groups, and hyperbolic invariants. The original motivation for the founders of knot theory was to create a table of knots and links, which are knots of several components entangled with each other. More than six billion knots and links have been tabulated since the beginnings of knot theory in the 19th century. To gain further insight, mathematicians have generalized the knot concept in several ways. Knots can be considered in other three-dimensional spaces and objects other than circles can be used; see knot (mathematics). A higher-dimensional knot is an n-dimensional sphere embedded in (n+2)-dimensional Euclidean space. (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)
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
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
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)
Knots and Quantum Theory - Edward Witten
Edward Witten Institute for Advanced Study December 15, 2010 A knot is simply a tangled loop in ordinary three-dimensional space, such as often causes us frustration in everyday life. Knots are also the subject of a rather rich mathematical theory. In the last three decades, it has unexpec
From playlist Natural Sciences
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)
Hyperbolic Knot Theory (Lecture - 1) by Abhijit Champanerkar
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)
Knots, Virtual Knots and Virtual Knot Cobordism by Louis H. Kauffman
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)
Sir Michael Atiyah - The Mysteries of Space [1991]
The 64th annual Gibbs Lecture was given by Sir Michael Atiyah, Fellow of the Royal Society, of Trinity College, Cambridge, England. At a conference in San Francisco, California in January 1991, he delivered "Physics and the mysteries of space", which was filmed and made available on videot
From playlist Mathematics
Knots and Quantum Theory | Edward Witten, Charles Simonyi Professor
Edward Witten, Charles Simonyi Professor, School of Natural Sciences, Institute for Advanced Study http://www.ias.edu/people/faculty-and-emeriti/witten A knot is more or less what you think it is—a tangled mess of string in ordinary three-dimensional space. In the twentieth century, mathe
From playlist Natural Sciences
Topologically Ordered Matter and Why You Should be Interested by Steven H. Simon
COLLOQUIUM TOPOLOGICALLY ORDERED MATTER AND WHY YOU SHOULD BE INTERESTED SPEAKER: Steven H. Simon (Oxford University, United Kingdom) DATE: Mon, 26 October 2020, 15:30 to 17:00 VENUE: Online ABSTRACT In two dimensional topologically ordered matter, processes depend on gross topology
From playlist ICTS Colloquia
How Knots Help Us Understand the World
Knots are everywhere in our daily lives, but a new branch of mathematics is taking things to the next level. Hosted by: Hank Green SciShow has a spinoff podcast! It's called SciShow Tangents. Check it out at http://www.scishowtangents.org ---------- Support SciShow by becoming a patron o
From playlist Uploads
A conversation between Louis Kauffman and Stephen Wolfram at the Wolfram Summer School 2021
Stephen Wolfram plays the role of Salonnière in this new, on-going series of intellectual explorations with special guests. Watch all of the conversations here: https://wolfr.am/youtube-sw-conversations Follow us on our official social media channels. Twitter: https://twitter.com/Wolfra
From playlist Conversations with Special Guests
Knots, three-manifolds and instantons – Peter Kronheimer & Tomasz Mrowka – ICM2018
Plenary Lecture 11 Knots, three-manifolds and instantons Peter Kronheimer & Tomasz Mrowka Abstract: Over the past four decades, input from geometry and analysis has been central to progress in the field of low-dimensional topology. This talk will focus on one aspect of these developments
From playlist Plenary Lectures
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
Jessica Purcell: Triangulations, geometry and knots
In this research profile, upcoming SMRI visitor Jessica Purcell describes the open questions in the study of 3-manifolds and how her fascination with mathematical knots began. Jessica Purcell is a Professor in the School of Mathematical Sciences and Associate Dean of Research (Faculty of
From playlist SMRI Interviews
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