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
Computational Aspects in the Braid Group and Applications to Cryptography - Mina Teicher
Mina Teicher Bar-Ilan University; Member, School of Mathematics March 12, 2012 The braid group on n strands may be viewed as an infinite analog of the symmetric group on n elements with additional topological phenomena. It appears in several areas of mathematics, physics and computer scien
From playlist Mathematics
Introduction to Fiber Bundles part 2: Structure Groups
This is an important notion where we the transition functions of a certain fiber bundles lie in a smaller subgroup. This is important for setting up Streenrod's theorem.
From playlist Fiber bundles
Link: https://www.geogebra.org/m/a72HSgzU
From playlist Geometry: Challenge Problems
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
Group Theory II Symmetry Groups
Why are groups so popular? Well, in part it is because of their ability to characterise symmetries. This makes them a powerful tool in physics, where symmetry underlies our whole understanding of the fundamental forces. In this introduction to group theory, I explain the symmetry group of
From playlist Foundational Math
Link: https://www.geogebra.org/m/bd69d6u4
From playlist Geometry: Challenge Problems
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, 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
Joel Hass - Lecture 1 - Algorithms and complexity in the theory of knots and manifolds - 18/06/18
School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Joel Hass (University of California at Davis, USA) Algorithms and complexity in the theory of knots and manifolds Abstract: These lectures will introduce algorithmic pro
From playlist Joel Hass - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects
Graham ELLIS - Computational group theory, cohomology of groups and topological methods 3
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Overview of Knots and Motivation of Quandels 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 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
Allison Moore - Essential Conway spheres and Floer homology via immersed curves
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Allison Moore, Virginia Commonwealth University Title: Essential Conway spheres and Floer homology via immersed curves Abstract: We consider the problem of whether Dehn surgery along a knot in the three-sphere produces an
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
Rebekah Palmer: Totally Geodesic Surfaces in Knot Complements with Small Crossing Number
Rebekah Palmer, Temple University Title: Totally Geodesic Surfaces in Knot Complements with Small Crossing Number Studying totally geodesic surfaces has been essential in understanding the geometry and topology of hyperbolic 3-manifolds. Recently, Bader-Fisher-Miller-Stover showed that con
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)
Matthew Hedden - Irreducible homology S1xS2's which aren't zero surgeries on a knot
June 20, 2018 - This talk was part of the 2018 RTG mini-conference Low-dimensional topology and its interactions with symplectic geometry I'll discuss constructions of manifolds with the homology of S^1xS^2 which don't arise as Dehn surgery on a knot in S^3. Our examples have weight one
From playlist 2018 RTG mini-conference on low-dimensional topology and its interactions with symplectic geometry I
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
Link: https://www.geogebra.org/m/JEk3MHvc
From playlist Geometry: Challenge Problems