Clifford algebras | Representation theory
In mathematics, a Clifford module is a representation of a Clifford algebra. In general a Clifford algebra C is a central simple algebra over some field extension L of the field K over which the quadratic form Q defining C is defined. The abstract theory of Clifford modules was founded by a paper of M. F. Atiyah, R. Bott and Arnold S. Shapiro. A fundamental result on Clifford modules is that the Morita equivalence class of a Clifford algebra (the equivalence class of the category of Clifford modules over it) depends only on the signature p − q (mod 8). This is an algebraic form of Bott periodicity. (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
Linear Algebra 19m: Matrix Representation of a LT - Vectors in ℝⁿ, Eigenbasis
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
Math 060 Linear Algebra 18 102214: Matrix Representations of Linear Transformations (part 3)
Matrix representations of linear transformations between Euclidean spaces, using non-standard bases.
From playlist Course 4: Linear 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 8e: A 3x3 Linear System
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 6j: Linear Systems for the Impatient
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
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
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"
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
Linear Algebra 11p: Some Matrices Are Not Invertible - I.e. They Don't Have an Inverse
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 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
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
Linear Algebra 6i: Linear Dependence Example 5 - Vectors in ℝⁿ
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
Lisa Glaser: A picture of a spectral triple
Talk at the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: A compact manifold can be described through a spectral triple, consisting of a Hilbert space H, an algebra of functions A and a Dirac operator D. But what if we are g
From playlist Noncommutative geometry meets topological recursion 2021
Yanli Song: K-theory of the reduced C*-algebra of a real reductive Lie group
Talk by Yanli Song in Global Noncommutative Geometry Seminar (Americas) on January 28, 2022 in https://globalncgseminar.org/talks/tba-23/
From playlist Global Noncommutative Geometry Seminar (Americas)
Ben Howard: Supersingular points on som orthogonal and unitary Shimura varieties
To an orthogonal group of signature (n,2), or to a unitary group of any signature, one can attach a Shimura variety. The general problem is to describe the integral models of these Shimura varieties, and their reductions modulo various primes. I will give a conjectural description of the s
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part4)
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
Linear Algebra 19b: Component Spaces - Doing It Right!
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
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