Lattice points | Quadratic forms | E8 (mathematics)
In mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive-definite, even, unimodular lattice of rank 8. The name derives from the fact that it is the root lattice of the E8 root system. The norm of the E8 lattice (divided by 2) is a positive definite even unimodular quadratic form in 8 variables, and conversely such a quadratic form can be used to construct a positive-definite, even, unimodular lattice of rank 8.The existence of such a form was first shown by H. J. S. Smith in 1867, and the first explicit construction of this quadratic form was given by Korkin and Zolotarev in 1873.The E8 lattice is also called the Gosset lattice after Thorold Gosset who was one of the first to study the geometry of the lattice itself around 1900. (Wikipedia).
AQA A-Level Further Maths C10-01 Eigenvalues and Eigenvectors: Introduction
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From playlist AQA A-Level Further Maths C10: Eigenvalues and Eigenvectors
Supermicro E300-9D-4CN8TP with Intel Xeon D-2123IT Review
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From playlist Cool Server Hardware Series
Physics 50 E&M Radiation (9 of 33) Plane E&M Waves
Visit http://ilectureonline.com for more math and science lectures! In this video I will mathematically explain electromagnetic radiation. Next video in series: http://youtu.be/oFRCRk7-j1o
From playlist PHYSICS 50 ELECTROMAGNETIC RADIATION
AQA A-Level Further Maths C10-07 Eigenvalues and Eigenvectors: 3D Example 3
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From playlist AQA A-Level Further Maths C10: Eigenvalues and Eigenvectors
Counting points on the E8 lattice with modular forms (theta functions) | #SoME2
In this video, I show a use of modular forms to answer a question about the E8 lattice. This video is meant to serve as an introduction to theta functions of lattices and to modular forms for those with some knowledge of vector spaces and series. -------------- References: (Paper on MIT
From playlist Summer of Math Exposition 2 videos
Modular forms: Theta functions in higher dimensions
This lecture is part of an online graduate course on modular forms. We study theta functions of even unimodular lattices, such as the root lattice of the E8 exceptional Lie algebra. As examples we show that one cannot "her the shape of a drum", and calculate the number of minimal vectors
From playlist Modular forms
A-Level Maths: E6-08 Compound Angles: EXTENSION Triple Angle Formulae
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From playlist A-Level Maths E6: Compound Angles & Equivalent Forms
Sphere packings in 8 dimensions (after Maryna Viazovska)
The is a math talk about the best possible sphere packing in 8 dimensions. It was an open problem for many years to show that the best 8-dimensional sphere packing is given by the E8 lattice. We describe the solution to this found by Maryna Viazovska, building on work of Henry Cohn and Noa
From playlist Math talks
From playlist Tutorial 8
How to construct the Leech lattice
This lecture describes an astonishingly simple construction of the Leech lattice in 24 dimensions, found by John Conway and Neal Sloane. This is an experimental joint video with @Lyam Boylan (https://www.tiktok.com/@yamsox/video/7057530890381053189) who added the animation, the thumbnai
From playlist Math talks
Linear Algebra 5.1.2 More About Eigenvectors and Eigenvalues
Proofs for Eigenvalues located on the main diagonal of a triangular matrix and for linear independence of eigenvectors.
From playlist Linear Algebra (Entire Course)
Some old Problems on the Lattice using Tensors by Raghav Jha
PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II
From playlist NUMSTRING 2022
This is an informal talk on sporadic groups given to the Archimedeans (the Cambridge undergraduate mathematical society). It discusses the classification of finite simple groups and some of the sporadic groups, and finishes by briefly describing monstrous moonshine. For other Archimedeans
From playlist Math talks
AQA A-Level Further Maths C11-06 Diagonalisation: Example 3
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From playlist AQA A-Level Further Maths C11: Diagonalisation
Complex surfaces 3: Rational surfaces
We give an informal survey of some complex rational surfaces. We first lift a few examples: hypersurfaces of degree at most 3, and the Hirzebruch surfaces which are P1 bundles over P1. Then we discuss the surfaces obtained by blowing up points in the plane in more detail. We sketch how to
From playlist Algebraic geometry: extra topics
70-680 : Windows 7 cipher.exe and EFS
More videos like tis online at http://www.theurbanpenguin.com In this video we explore the strength of using the command line when using the Encrypted File system, EFS, in Windows 7. As Microsoft encourages technicians to be familiar with the command line tools this may become a topic in y
From playlist 70-680
Giuseppe Mussardo - 2D Ising Model and its tricritical version, when theory meets experiments
The magnetic deformation of the 2D Ising Model and the thermal deformation of the Tricritical Ising Model are related to the exceptional E_8 and E_7 Lie algebras. The corresponding exact S-matrix theories and the related dynamical structure factors of both models have a rich spectroscopy
From playlist 100…(102!) Years of the Ising Model
AQA A-Level Further Maths C10-02 Eigenvalues and Eigenvectors: Formalising Notation & Method
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From playlist AQA A-Level Further Maths C10: Eigenvalues and Eigenvectors
This is a historical talk giving my recollections of how vertex algebras were discovered. It was requested by Michael Penn for his series of videos on vertex algebras https://www.youtube.com/playlist?list=PL22w63XsKjqyx2FFUywi_mz91Jtih52yX
From playlist Math talks