LC001.03 - Clifford algebras and matrix factorisations
A brief introduction to Clifford algebras, their universal property, how to construct a Clifford algebra from the Hessian of a quadratic form, and how modules over that Clifford algebra determine matrix factorisations. This video is a recording made in a virtual world (https://www.roblox.
From playlist Metauni
Geometric Algebra in 2D - Fundamentals and Another Look at Complex Numbers
In this video, I introduce some of the concepts of geometric (Clifford) algebra, focusing on two-dimensional space (R^2). We'll talk about the wedge (exterior) product, review the dot product, and introduce the geometric product. We'll see that a new mathematical object, the bivector, aris
From playlist Math
Matrix Algebra Basics || Matrix Algebra for Beginners
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. This course is about basics of matrix algebra. Website: https://geekslesson.com/ 0:00 Introduction 0:19 Vectors and Matrices 3:30 Identities and Transposes 5:59 Add
From playlist Algebra
Linear Algebra 2e: Confirming All the 'Tivities
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications
Linear Algebra Full Course for Beginners to Experts
Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis may be basically viewed as the application of l
From playlist Linear Algebra
Geometric Algebra - The Matrix Representation of a Linear Transformation
In this video, we will show how matrices as computational tools may conveniently represent the action of a linear transformation upon a given basis. We will prove that conventional matrix operations, particularly matrix multiplication, conform to the composition of linear transformations.
From playlist Geometric Algebra
Linear Algebra 2q: Summary of Terms Encountered so Far
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications
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
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
Taylor Dupuy | Spheres Packings in Hyperbolic Space
African Mathematics Seminar | 2 September 2020 Virtually hosted by the University of Nairobi Visit our webpage: https://sites.google.com/view/africa-math-seminar Sponsor: International Science Programme
From playlist Seminar Talks
Matrix factorisations and quantum error correcting codes
In this talk Daniel Murfet gives a brief introduction to matrix factorisations, the bicategory of Landau-Ginzburg models, composition in this bicategory, the Clifford thickening of a supercategory and the cut operation, before coming to a simple example which shows the relationship between
From playlist Metauni
Christian Voigt: Clifford algebras, Fermions and categorification
Given the fundamental role of Dirac operators in K-homology and K-theory, it can be argued that "categorified Dirac operators" should be crucial for the understanding of elliptic cohomology. However, the actual construction of such operators seems a challenging open problem. In this talk
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part2)
We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of Bruinier-Yang and Buinier-Kudla-Yang which provide explicit formulas for the arithmetic intersecti
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Landau-Ginzburg - Seminar 5 - From quadratic forms to bicategories
This seminar series is about the bicategory of Landau-Ginzburg models LG, hypersurface singularities and matrix factorisations. In this seminar Dan Murfet starts with quadratic forms and introduces Clifford algebras, their modules and bimodules and explains how these fit into a bicategory
From playlist Metauni
G. Molino - The Horizontal Einstein Property for H-Type sub-Riemannian Manifolds
We generalize the notion of H-type sub-Riemannian manifolds introduced by Baudoin and Kim, and then introduce a notion of parallel Clifford structure related to a recent work of Moroianu and Semmelmann. On those structures, we prove an Einstein property for the horizontal distribution usin
From playlist Journées Sous-Riemanniennes 2018
Jeongwan Haah - Nontrivial Clifford QCAs - IPAM at UCLA
Recorded 01 September 2021. Jeongwan Haah of Microsoft Research presents "Nontrivial Clifford QCAs" at IPAM's Graduate Summer School: Mathematics of Topological Phases of Matter. Abstract: An interesting role of QCA is that it can disentangle a Hamiltonian while quantum circuits cannot. We
From playlist Graduate Summer School 2021: Mathematics of Topological Phases of Matter
Linear Algebra 16h7: Generalized Eigenvectors Example
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 3 Linear Algebra: Linear Transformations