Algebraic groups | Exceptional Lie algebras | Lie groups
In mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras , all of which have dimension 78; the same notation E6 is used for the corresponding root lattice, which has rank 6. The designation E6 comes from the Cartan–Killing classification of the complex simple Lie algebras (see Élie Cartan § Work). This classifies Lie algebras into four infinite series labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E6 algebra is thus one of the five exceptional cases. The fundamental group of the complex form, compact real form, or any algebraic version of E6 is the cyclic group Z/3Z, and its outer automorphism group is the cyclic group Z/2Z. Its fundamental representation is 27-dimensional (complex), and a basis is given by the 27 lines on a cubic surface. The dual representation, which is inequivalent, is also 27-dimensional. In particle physics, E6 plays a role in some grand unified theories. (Wikipedia).
Calculus 1: Ch 5.1 Derivative of e^x and lnx (3 of 24) What is the Number e?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the number “e”. e=2.718218284590..., “e” is called the natural number” because in nature things tend to increase and decrease according to that number. Some of the examples of that inc
From playlist CALCULUS 1 CH 5.1 DERIVATIVES e^x AND ln x
Calculus 1: Ch 5.1 Derivative of e^x and lnx (5 of 24) What is the number e ?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the mathematical definition of e=2.7182818284590... The definition is e=lim(x approaches infinity)[1+(1/x)] raised to the power of x. When x=1 e~2, x=2 e~2.25, x=3 e~2.370, x=4 e~2.441, x=5 e`
From playlist CALCULUS 1 CH 5.1 DERIVATIVES e^x AND ln x
What is the mathematical constant e???
In this video, I talk about two ways of "deriving" e and the important of the number! "Why do we study e?" is often over-shadowed by procedural grind, so here we explicitly talk about where it comes from and how it is used. It is important to note that I explained e *without* direct use of
From playlist Misc. / Why We Study Math
Linear Algebra 15: Eigenvalues and eigenvectors of a function (Ch6 Pr2)
How to compute the eigenvalues and eigenvectors of a function. Presented by Peter Brown from the UNSW School of Mathematics and Statistics.
From playlist MATH2501 - Linear Algebra
AQA A-Level Further Maths C10-01 Eigenvalues and Eigenvectors: Introduction
Navigate all of my videos at https://sites.google.com/site/tlmaths314/ Like my Facebook Page: https://www.facebook.com/TLMaths-1943955188961592/ to keep updated Follow me on Instagram here: https://www.instagram.com/tlmaths/ Many, MANY thanks to Dean @deanencoded for designing my openin
From playlist AQA A-Level Further Maths C10: Eigenvalues and Eigenvectors
Finding Eigenvalues and Eigenvectors
In studying linear algebra, we will inevitably stumble upon the concept of eigenvalues and eigenvectors. These sound very exotic, but they are very important not just in math, but also physics. Let's learn what they are, and how to find them! Script by Howard Whittle Watch the whole Math
From playlist Mathematics (All Of It)
A11 Eigenvalues with complex numbers
Eigenvalues which contain complex numbers.
From playlist A Second Course in Differential Equations
e is a magic number (song about e)
Fun with a math song all about the famous number e. Free ebook https://bookboon.com/en/engineering-mathematics-youtube-workbook-ebook E is a magic number by Dr Chris Tisdell e is a magic number, Yes it is, it's a magic number. All across our scientific community, You'll find e, 'cos it'
From playlist Math is Fun!
Retract rationality of some (exceptional) group varieties by Maneesh Thakur
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Insanely Hard High School Math Question - Online Math Olympiad Apple Tree Probability
The Online Math Olympiad is a contest for high school students with challenging problem. This 2016 test had an average score of 9 out of 30. This video is an adaption of problem 16 which is an interesting probability puzzle. At the end of day 0, six magical seeds are planted. On each day f
From playlist Statistics And Probability
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
Eisenstein Series on Exceptional Groups, Graviton Scattering Amplitudes... - Stephen Miller
Stephen D. Miller Rutgers, The State University of New Jersey May 3, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Discrete Math II - 10.3.1 Representing Graphs
In this SHORT video, we look at how to represent undirected graphs using adjacency and incidence matrices. Video Chapters: Intro 0:00 Adjacency Matrices 0:14 Incidence Matrices 3:09 Up Next 5:06 This playlist uses Discrete Mathematics and Its Applications, Rosen 8e Power Point slide d
From playlist Discrete Math II/Combinatorics (entire course)
Washington Taylor - How Natural is the Standard Model in the String Landscape?
Mike's pioneering work in taking a statistical approach to string vacua has contributed to an ever-improving picture of the landscape of solutions of string theory. In this talk, we explore how such statistical ideas may be relevant in understanding how natural different realizations of th
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
Joel Kamnitzer - Symplectic Resolutions, Coulomb Branches, and 3d Mirror Symmetry 2/5
In the 21st century, there has been a great interest in the study of symplectic resolutions, such as cotangent bundles of flag varieties, hypertoric varieties, quiver varieties, and affine Grassmannian slices. Mathematicians, especially Braden-Licata-Proudfoot-Webster, and physicists obser
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Antun Milas: Graphs, quivers and vertex algebra characters
CONFERENCE Recorded during the meeting "Vertex Algebras and Representation Theory" the June 07, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's A
From playlist Mathematical Physics
This lecture is part of an online graduate course on modular forms. We first show that the number of zeros of a (level 1 holomorphic) modular form in a fundamental domain is weight/12, and use this to show that the graded ring of modular forms is the ring of polynomials in E4 and E6. Fo
From playlist Modular forms
Geometry: Ch 5 - Proofs in Geometry (2 of 58) Definitions
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and give examples of definitions. Next video in this series can be seen at: https://youtu.be/-Pmkhgec704
From playlist GEOMETRY 5 - PROOFS IN GEOMETRY
Thomas Krämer: Big monodromy on abelian varieties: How to deal with wedge powers
CONFERENCE Recorded during the meeting "D-Modules: Applications to Algebraic Geometry, Arithmetic and Mirror Symmetry" the April 11, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by
From playlist Algebraic and Complex Geometry