Diagram algebras | Operator algebras | Knot theory
In mathematics, planar algebras first appeared in the work of Vaughan Jones on the standard invariant of a II1 subfactor. They also provide an appropriate algebraic framework for many knot invariants (in particular the Jones polynomial), and have been used in describing the properties of Khovanov homology with respect to tangle composition. Any subfactor planar algebra provides a family of unitary representations of Thompson groups.Any finite group (and quantum generalization) can be encoded as a planar algebra. (Wikipedia).
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Algebra for Beginners | Basics of Algebra
#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten
From playlist Linear Algebra
This is part of an online course on beginner/intermediate linear algebra, which presents theory and implementation in MATLAB and Python. The course is designed for people interested in applying linear algebra to applications in multivariate signal processing, statistics, and data science.
From playlist Linear algebra: theory and implementation
Using the general and vector forms of the equation of a plane from the normal and a point, or two points on the plane.
From playlist Linear Algebra
7A_2 Linear Algebra Definitions
"linear algebra" "matrix equations" "linear set" "set linear equations" linear algebra matrix equation linear set equations "triangular matrix" "square matrix" "main diagonal" homogenous consistent triangular square "elemetary matrix" elementary row echelon reduced
From playlist Linear Algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions and their representations through matrices and vector spaces. Linear algebra is central to almost all areas of mathematics. Topic covered: Vectors: Basic vectors notation, adding, scaling (0:0
From playlist Linear Algebra
RNT1.4. Ideals and Quotient Rings
Ring Theory: We define ideals in rings as an analogue of normal subgroups in group theory. We give a correspondence between (two-sided) ideals and kernels of homomorphisms using quotient rings. We also state the First Isomorphism Theorem for Rings and give examples.
From playlist Abstract Algebra
Hierarchies of contact manifolds via rational SFT - Zhengyi Zhou
IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: Hierarchies of contact manifolds via rational SFT Speaker: Zhengyi Zhou Affiliation: Member, School of Mathematics Date: December 11, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Hierarchies of contact manifolds - Zhengyi Zhou
Short Talks by Postdoctoral Members Topic: Hierarchies of contact manifolds Speaker: Zhengyi Zhou Affiliation: Member, School of Mathematics Date: October 1, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Forbidden Patterns in Tropical Planar Curves by Ayush Kumar Tewari
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME 27 June 2022 to 08 July 2022 VENUE Madhava Lecture Hall and Online Algebraic geometry is the stu
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Vaughan Jones: “What is it about the Plane?”
Green Family Lecture Series 2018 “What is it about the Plane?” Vaughan Jones, Vanderbilt University Abstract: We write and draw on paper, flat. We watch movies on screens, flat. We project 3 dimensional structures onto the plane, flat. From antiquity on, the plane has been key to our und
From playlist Public Lectures
Planar N = 4 at High Loops and Large Multiplicity by Andrew McLeod
PROGRAM RECENT DEVELOPMENTS IN S-MATRIX THEORY (ONLINE) ORGANIZERS: Alok Laddha, Song He and Yu-tin Huang DATE: 20 July 2020 to 31 July 2020 VENUE:Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through online
From playlist Recent Developments in S-matrix Theory (Online)
This is Lecture 22 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2022.pdf More information may
From playlist CSE547 - Discrete Mathematics - 1999 SBU
Ralph KAUFMANN - Categorical Interactions in Algebra, Geometry and Physics
Categorical Interactions in Algebra, Geometry and Physics: Cubical Structures and Truncations There are several interactions between algebra and geometry coming from polytopic complexes as for instance demonstrated by several versions of Deligne's conjecture. These are related through bl
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Topology, Winding Numbers and Signed Area | Algebraic Calculus One | Wild Egg
Topology arises from a key property of the continuum as modelled by the rational numbers: that we have distinguished positive numbers (x greater than or equal to 0) which are closed under addition and multiplication. This is the starting point of notions of inside and outside. When we mov
From playlist Algebraic Calculus One from Wild Egg
J. Aramayona - MCG and infinite MCG (Part 3)
The first part of the course will be devoted to some of the classical results about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston classification, abelianization, isomorphic rigidity, geometry of combinatorial models. In the secon
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
8 Row and Column Views of a Matrix
The row and column view of a system of linear equations, as well as the matrix as a mathematical object.
From playlist Linear Algebra
Marcy Robertson: Expansions, completions and automorphisms of welded tangled foams
SMRI Seminar: Marcy Robertson (University of Melbourne) Abstract: Welded tangles are knotted surfaces in R^4. Bar-Natan and Dancso described a class of welded tangles which have "foamed vertices" where one allows surfaces to merge and split. The resulting welded tangled foams carry an alg
From playlist SMRI Seminars
13E A Matrix Equation for the Dot Product
Writing the Euclidean inner product in the form of matrix multiplication.
From playlist Linear Algebra