In the mathematical field of knot theory, an algebraic link is a link that can be decomposed by Conway spheres into 2-tangles. Algebraic links are also called arborescent links.Although algebraic links and algebraic tangles were originally defined by John H. Conway as having two pairs of open ends, they were subsequently generalized to more pairs. (Wikipedia).
23 Algebraic system isomorphism
Isomorphic algebraic systems are systems in which there is a mapping from one to the other that is a one-to-one correspondence, with all relations and operations preserved in the correspondence.
From playlist Abstract algebra
Algebraic topology: Introduction
This lecture is part of an online course on algebraic topology. This is an introductory lecture, where we give a quick overview of some of the invariants of algebraic topology (homotopy groups, homology groups, K theory, and cobordism). The book "algebraic topology" by Allen Hatcher men
From playlist Algebraic topology
Equivalence Relations Definition and Examples
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Equivalence Relations Definition and Examples. This video starts by defining a relation, reflexive relation, symmetric relation, transitive relation, and then an equivalence relation. Several examples are given.
From playlist Abstract Algebra
A Peek at Signed Areas: The Algebraic Calculus One course
The Algebraic Calculus One course is purely online at Open Learning, and gives a novel and careful approach to the classical subject of Calculus, but without infinite processes or real numbers. In this video we have a look at the course, in particular the Chapter on Signed Areas, which giv
From playlist Algebraic Calculus One Info
AlgTopReview3: More on commutative groups---isomorphisms, homomorphisms, cosets and quotient groups
We present more information on commutative groups and the fundamental structure theorem that every such group is isomorphic to a direct sum of cyclic groups Z_n. We discuss the notions of isomorphism, homomorphism, cosets of a subgroup, and the quotient of a group by a subgroup. *********
From playlist Algebraic Topology
An introduction to homology (cont.) | Algebraic Topology | NJ Wildberger
Here we carry on our introduction to homology, focussing on a particularly simple space, basically a graph and various modifications to it. We discuss cycles, boundaries, and homology as a quotient of cycles mod boundaries, one such group for each dimension. The framework is commutative g
From playlist Algebraic Topology
AlgTopReview: An informal introduction to abstract algebra
This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is
From playlist Algebraic Topology
A Tour of Skein Modules by Rhea Palak Bakshi
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)
A bordered approach to link Floer homology - Peter Ozsváth
IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: A bordered approach to link Floer homology Speaker: Peter Ozsváth Affiliation: Princeton University Date: July 10, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
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
Eugene Gorsky - Algebra and geometry of link homology 4/5
Khovanov and Rozansky defined a link homology theory which categorifies the HOMFLY-PT polynomial. This homology is relatively easy to define, but notoriously hard to compute. I will discuss recent breakthroughs in understanding and computing Khovanov-Rozansky homology, focusing on connecti
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Representations of Kauffman bracket skein algebras of a surface - Helen Wong
Members' Seminar Topic: Representations of Kauffman bracket skein algebras of a surface Speaker: Helen Wong Affiliation: Carleton University; von Neumann Fellow, School of Mathematics Date: November 20, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Juliet Cooke: Skein categories
In this talk we will talk about skein categories which are a categorical analogue of skein algebras based on coloured ribbon tangles. We shall then see how these skein categories satisfy excision and therefore fit within the framework of factorisation homology as k-linear factorisation hom
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Julien Marché: Differential equation for the Reidemeister torsion
Abstract: The Reidemeister torsion may be viewed as a volume form on the character variety of a 3-manifold with boundary. I will explain a conjectural differential equation that this form should satisfy, motivated by the study of the asymptotical behaviour of quantum invariants. Recording
From playlist Topology
Nezhla Aghaei - Combinatorial Quantisation of Supergroup Chern-Simons Theory
Chern-Simons Theories with gauge super-groups appear naturally in string theory and they possess interesting applications in mathematics, e.g. for the construction of knot and link invariants. In my talk, I will review the framework of combinatorial quantization of Chern Simons theory and
From playlist Workshop on Quantum Geometry
Become an Algebra Master in 30 Minutes a Day
Yes it is possible to become become an algebra master in just 30 minutes a day. It's all about being consistent and in time you will just get so much better! In this video I talk about how to do this from start to finish. My Course on College Algebra (Blitzer's College Algebra is a good
From playlist Book Reviews
Pierrick Bousseau - The Skein Algebra of the 4-punctured Sphere from Curve Counting
The Kauffman bracket skein algebra is a quantization of the algebra of regular functions on the SL_2 character of a topological surface. I will explain how to realize the skein algebra of the 4-punctured sphere as the output of a mirror symmetry construction based on higher genus Gromov-Wi
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Maria Chlouveraki, Research talk - 29 January 2015
Maria Chlouveraki (Université de Versailles - St Quentin) - Research talk http://www.crm.sns.it/course/4206/ Yokonuma-Hecke algebras were introduced by Yokonuma in the 60's as generalisations of Iwahori-Hecke algebras. They have recently attracted the interest of topologists, because the
From playlist Lie Theory and Representation Theory - 2015
AlgTop25: More on the fundamental group
A continuation on the fundamental group of a surface, we prove that the multiplication of equivalence classes or types of loops from a base point does indeed form a group in the algebraic sense. We discuss the fundamental group of the torus and the projective plane. This is part of a begi
From playlist Algebraic Topology