Algebraic groups | Exceptional Lie algebras | Lie groups | Octonions
In mathematics, G2 is the name of three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras as well as some algebraic groups. They are the smallest of the five exceptional simple Lie groups. G2 has rank 2 and dimension 14. It has two fundamental representations, with dimension 7 and 14. The compact form of G2 can be described as the automorphism group of the octonion algebra or, equivalently, as the subgroup of SO(7) that preserves any chosen particular vector in its 8-dimensional real spinor representation (a spin representation). (Wikipedia).
Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-
From playlist Abstract Algebra
A review of the notes common to all formations of a G chord.
From playlist Music Lessons
Chapter 4 - Solving Linear Equations with Technology - IB Math Studies (Math SL)
Hello and welcome to What The Math. This is a Chapter 4 video about linear equations and using GDC to solve various linear functions. This is a part of Chapter 4 from Harris Publication version of IB math book by Haese.
From playlist IB Math Studies Chapter 4
Group Theory: The Center of a Group G is a Subgroup of G Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Group Theory: The Center of a Group G is a Subgroup of G Proof
From playlist Abstract Algebra
Equivalence Relation on a Group Two Proofs
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Equivalence Relation on a Group Two Proofs. Given a group G and a subgroup H of G, we prove that the relation x=y if xy^{-1} is in H is an equivalence relation on G. Then cosets are defined and we prove that s_1 = s_2 iff [s_1] = [s
From playlist Abstract Algebra
Example of Group: GL(2, R) (3 of 3)
Abstract Algebra: Let G=GL(2, R) be the group of real invertible 2x2 matrices. We consider two group actions for the group GL(2, R) on itself. We interpret the results in terms of linear algebra and change of basis. We also explain how conjugacy classes of G relate to the diagonalizati
From playlist Abstract Algebra
SAT Math (Geometry) - Practice 3.8
The video provides an explanation of a practice SAT math question involving geometry. View or download the practice questions at http://www.ck12.org. Site: http://mathispower4u.com
From playlist SAT Math Practice
This video defines and gives and example of isomorphic graphs. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Block diagram algebra 2019-04-15
Understanding why you can't take the z transform of continuous systems in series
From playlist Discrete
Modular forms, G2, and Bloch-Kato (Sam Mundy) | Ep. 18
Sam Mundy is a number theorist and NSF postdoc at Princeton University. We discuss his new paper "Eisenstein series for G2 and the symmetric cube Bloch-Kato conjecture". The Bloch-Kato conjecture is a generalization of the Birch and Swinnerton-Dyer conjecture relating the order of vanishin
From playlist Daniel Rubin Show, Full episodes
Tutorial for Simon Caron-huot lectures by Yue-Zhou Li
PROGRAM KAVLI ASIAN WINTER SCHOOL (KAWS) ON STRINGS, PARTICLES AND COSMOLOGY (ONLINE) ORGANIZERS Francesco Benini (SISSA, Italy), Bartek Czech (Tsinghua University, China), Dongmin Gang (Seoul National University, South Korea), Sungjay Lee (Korea Institute for Advanced Study, South Korea
From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology (ONLINE) - 2022
An Oxford Mathematics Graduate Supervision - Geometry and Physics in 7 Dimensions
So how do supervisor & graduate student work together? What happens in a graduate supervision? To find out, we filmed a supervision. Introducing Professor Jason Lotay & graduate student Izar Alonso Lorenzo as they discuss geometry in seven dimensions related to special holonomy, gauge the
From playlist Oxford Mathematics Student Tutorials and Graduate Supervisions
MIT 8.422 Atomic and Optical Physics II, Spring 2013 View the complete course: http://ocw.mit.edu/8-422S13 Instructor: Wolfgang Ketterle In this lecture, the professor discussed g(2) for atoms and light, classical vs. quantum statistics, etc. License: Creative Commons BY-NC-SA More infor
From playlist MIT 8.422 Atomic and Optical Physics II, Spring 2013
Slava Rychkov - Random Field Ising Model and Parisi-Sourlas Supersymmetry (4/4)
Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any d. I will present a recent theory, developed in 2019
From playlist Slava Rychkov - Random Field Ising Model and Parisi-Sourlas Supersymmetry
ISOMORPHISMS and BIPARTITE GRAPHS - DISCRETE MATHEMATICS
In this video we look at isomorphisms of graphs and bipartite graphs. We also look at complete bipartite graphs and their complements. Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/play
From playlist Discrete Math 2
MATH1011 Section 3.1 Question 8
In this video we find a function g(x) given g'(x). Presented by Thanom Shaw of the School of Mathematics and Statistics, UNSW.
From playlist MATH1011 Calculus Problems
Pre-recorded lecture 22: Open problems (part 2)
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Huajie Chen - Convergence of the Planewave Approximations for Quantum Incommensurate Systems
Recorded 04 May 2022. Huajie Chen of Beijing Normal University, School of Mathematical Sciences, presents "Convergence of the Planewave Approximations for Quantum Incommensurate Systems" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Abstract: We study the
From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics
Lorenzo Foscolo: ALC manifolds with exceptional holonomy
We will describe the construction of complete non-compact Ricci-flat manifolds of dimension 7 and 8 with holonomy $G_{2}$ and Spin(7) respectively. The examples we consider all have non-maximal volume growth and an asymptotic geometry, so-called ALC geometry, that generalises to higher dim
From playlist Geometry
What is a Subgraph? | Graph Theory
What is a subgraph? We go over it in today's math lesson! If you're familiar with subsets, then subgraphs are probably exactly what you think they are. Recall that a graph G = (V(G), E(G)) is an ordered pair with a vertex set V(G) and an edge set E(G). Then, another graph H = (V(H), E(H))
From playlist Graph Theory