Free ebook http://tinyurl.com/EngMathYT A basic introduction to the curl of a vector field - one of the basic operations of vector calculus. I show how to calculate the curl and discuss its relationship with rotation and circulation density. Many examples are presented.
From playlist Engineering Mathematics
TQFTs from non-semisimple modular categories and modified traces, Marco de Renzi, Lecture II
Lecture series on modified traces in algebra and topology Topological Quantum Field Theories (TQFTs for short) provide very sophisticated tools for the study of topology in dimension 2 and 3: they contain invariants of 3-manifolds that can be computed by cut-and-paste methods, and their e
From playlist Lecture series on modified traces in algebra and topology
Linear Equations from the Graph of the Line, No. 1
Shows how to write the equation of a line in the slope intercept from from the graph of the line. You can link to all my videos at my website: https://www.stepbystepscience.com
From playlist Algebra; Linear Equations
Michael BORINSKY - The Euler Characteristic of Out(Fn) and the Hopf Algebra of Graphs
In their 1986 work, Harer and Zagier gave an expression for the Euler characteristic of the moduli space of curves, M_gn, or equivalently the mapping class group of a surface. Recently, in joint work with Karen Vogtmann, we performed a similar analysis for Out(Fn), the outer automorphism g
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Claudia Pinzari: "Weak quasi-Hopf algebras associated to Verlinde fusion categories"
Actions of Tensor Categories on C*-algebras 2021 "Weak quasi-Hopf algebras associated to Verlinde fusion categories" Claudia Pinzari - Sapienza Università di Roma Abstract: Unitary modular fusion categories arise in various frameworks. After a general overview on unitarity, we discuss th
From playlist Actions of Tensor Categories on C*-algebras 2021
In this video I write down the axioms of Lie algebras and then discuss the defining anti-symmetric bilinear map (the Lie bracket) which is zero on the diagonal and fulfills the Jacobi identity. I'm following the compact book "Introduction to Lie Algebras" by Erdmann and Wildon. https://gi
From playlist Algebra
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
Paul André Melliès - Dialogue Games and Logical Proofs in String Diagrams
After a short introduction to the functorial approach to logical proofs and programs initiated by Lambek in the late 1960s, based on the notion of free cartesian closed category, we will describe a recent convergence with the notion of ribbon category introduced in 1990 by Reshetikhin and
From playlist Combinatorics and Arithmetic for Physics: 02-03 December 2020
Simple intro to the curl of a vector field and how to calculate it. The curl is one of the basic operations of vector calculus.
From playlist Engineering Mathematics
Linear algebra: Prove the Sherman-Morrison formula for computing a matrix inverse
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
[BOURBAKI 2019] HOMFLY polynomials from the Hilbert schemes of a planar curve - Migliorini -30/03/19
Luca MIGLIORINI HOMFLY polynomials from the Hilbert schemes of a planar curve, after D. Maulik, A. Oblomkov, V. Shende... Among the most interesting invariants one can associate with a link L ⊂ S3 is its HOMFLY polynomial P(L, v, s) ∈ Z[v±1, (s – s–1)±1]. A. Oblomkov and V. Shende conjec
From playlist BOURBAKI - 2019
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
An introduction to modified traces, Jonathan Kujawa, Lecture II
Lecture series on modified traces in algebra and topology The trace of a map and the dimension of a representation are fundamental invariants in representation theory. They are useful both for proving results in representation theory and for applications in other areas (e.g., low-dimensio
From playlist Lecture series on modified traces in algebra and topology
Beauty and Truth in Mathematics; a Tribute to Albert Einstein and Hermann Weyl - Sir Michael Atiyah
Sir Michael Atiyah Institute for Advanced Study November 8, 2010 For more videos, visit http://video.ias.edu
From playlist Mathematics
Example of Gram-Schmidt Orthogonalization
Linear Algebra: Construct an orthonormal basis of R^3 by applying the Gram-Schmidt orthogonalization process to (1, 1, 1), (1, 0, 1), and (1, 1, 0). In addition, we show how the Gram-Schmidt equations allow one to factor an invertible matrix into an orthogonal matrix times an upper tria
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
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
An introduction to modified traces, Jonathan Kujawa, Lecture III
The trace of a map and the dimension of a representation are fundamental invariants in representation theory. They are useful both for proving results in representation theory and for applications in other areas (e.g., low-dimensional topology). Unfortunately, in the non-semi-simple settin
From playlist Lecture series on modified traces in algebra and topology
The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature
In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932
From playlist Algebra
The GrassmannCalculus application, based on the work of Grassmann and Browne, is described. One example, the derivation of coordinate equations for lines and planes in n-dimensional space, is presented. This illustrates how smoothly Mathematica and Grassmann–Browne algebra merge to form a
From playlist Wolfram Technology Conference 2021
Lie groups: Baker Campbell Hausdorff formula
This lecture is part of an online graduate course on Lie groups. We state the Baker Campbell Hausdorff formula for exp(A)exp(B). As applications we show that a Lie group is determined up to local isomorphism by its Lie algebra, and homomorphisms from a simply connected Lie group are deter
From playlist Lie groups