Manifolds | Links (knot theory)
In mathematical knot theory, a link is a collection of knots which do not intersect, but which may be linked (or knotted) together. A knot can be described as a link with one component. Links and knots are studied in a branch of mathematics called knot theory. Implicit in this definition is that there is a trivial reference link, usually called the unlink, but the word is also sometimes used in context where there is no notion of a trivial link. For example, a co-dimension 2 link in 3-dimensional space is a subspace of 3-dimensional Euclidean space (or often the 3-sphere) whose connected components are homeomorphic to circles. The simplest nontrivial example of a link with more than one component is called the Hopf link, which consists of two circles (or unknots) linked together once. The circles inthe Borromean rings are collectively linked despite the fact that no two of them are directly linked. The Borromean rings thus form a Brunnian link and in fact constitute the simplest such link. (Wikipedia).
What are Connected Graphs? | Graph Theory
What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
From playlist Graph Theory
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
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
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
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)
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
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
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
Primes and Knots - Akshay Venkatesh
Public Lecture: Primes and Knots - October 25, 2019 Akshay Venkatesh, Robert and Luisa Fernholz Professor School of Mathematics, IAS In mathematics, there are many surprising parallels between problems in the theory of numbers and questions in three-dimensional geometry. Akshay Venkatesh
From playlist Mathematics
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)
Andreas Zastrow: An Embedded Circle into R3 Might Escape Before an Isotoped Linked Circle
Andreas Zastrow, University of Gdansk (Inst. Math.) Title: An Embedded Circle into R3 Might Not Be Able to Escape Before an Isotoped Linked Circle The mathematically precise statement of the problem that was intuitively described in the title is following isotopy-extension problem: Given t
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
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
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
Nicholas Cazet: Surface-link Families with Arbitrarily Large Triple Point Number
Nicholas Cazet, UC Davis Title: Surface-link Families with Arbitrarily Large Triple Point Number Analogous to a classical knot diagram, a surface-knot can be generically projected to 3-space and given crossing information to create a broken sheet diagram. A generic compact surface in 3-spa
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Hyperbolic Knot Theory (Lecture - 2) 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)
Solving a fascinating puzzle using Knot Theory and Free Groups | #SoME2
Combining Knot Theory with Free Groups with the aim of tackling a difficult mathematical puzzle. Timeline: 00:00 - Intro 00:50 - Definition of mathematical knots 01:57 - Equivalent knots 03:28 - Knot links 04:32 - Puzzle, the base case 06:38 - Generalization using knots 08:54 - Connectio
From playlist Summer of Math Exposition 2 videos
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)