The Lie-algebra of Quaternion algebras and their Lie-subalgebras
In this video we discuss the Lie-algebras of general quaternion algebras over general fields, especially as the Lie-algebra is naturally given for 2x2 representations. The video follows a longer video I previously did on quaternions, but this time I focus on the Lie-algebra operation. I st
From playlist Algebra
In this video I write down the axioms of Lie algebras and then discuss the defining anti-symmetric bilinear map (the Lie bracket) which is zero on the diagonal and fulfills the Jacobi identity. I'm following the compact book "Introduction to Lie Algebras" by Erdmann and Wildon. https://gi
From playlist Algebra
MATH1131 Linear Algebra: Chapter 1 Problem 41 iv
We find a parametric vector form of a plane given by a single Cartesian equation. Presented by N J Wildberger of the School of Mathematics and Statistics, Faculty of Science, UNSW.
From playlist Mathematics 1A (Algebra)
Convert a Cartesian Plane into Parametric Vector Form (Ch1 Pr41d)
In this video we derive a parametric vector form for a plane in 3D in two different ways: visually and using some algebra. This is Chapter 1, Problem 41 d) of our MATH1141 Algebra notes. Presented by Daniel Mansfield of the School of Mathematics and Statistics, UNSW.
From playlist Mathematics 1A (Algebra)
This lecture is part of an online graduate course on Lie groups. We define the Lie algebra of a Lie group in two ways, and show that it satisfied the Jacobi identity. The we calculate the Lie algebras of a few Lie groups. For the other lectures in the course see https://www.youtube.co
From playlist Lie groups
Linearly Parametrized Curves | Algebraic Calculus One | Wild Egg
Parametrized curves figure prominently in the Algebraic Calculus, and they coincide with de Casteljau Bezier curves. The simplest case are the linearly parametrized curves given by a pair of linear polynomials of polynumbers. This gives us an alternate view of oriented polygonal splines.
From playlist Algebraic Calculus One
Algebra for Beginners | Basics of Algebra
#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten
From playlist Linear Algebra
Determining if a vector is a linear combination of other vectors
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Determining if a vector is a linear combination of other vectors
From playlist Linear Algebra
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
Higgs bundles and higher Teichmüller components (Lecture 2) by Oscar García-Prada
DISCUSSION MEETING : MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE : 10 February 2020 to 14 February 2020 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classif
From playlist Moduli Of Bundles And Related Structures 2020
Perverse sheaves on configuration spaces, Hopf algebras and parabolic induction - Mikhail Kapranov
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Perverse sheaves on configuration spaces, Hopf algebras and parabolic induction Speaker: Mikhail Kapranov Affiliation: Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo Dat
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Representations of finite groups of Lie type (Lecture - 3) by Dipendra Prasad
PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund
From playlist Group Algebras, Representations And Computation
Representations of finite groups of Lie type (Lecture 2) by Dipendra Prasad
PROGRAM : GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fun
From playlist Group Algebras, Representations And Computation
Geometric deformations of orthogonal and symplectic Galois representations - Jeremy Booher
Jeremy Booher Stanford University November 19, 2015 https://www.math.ias.edu/seminars/abstract?event=87395 For a representation of the absolute Galois group of the rationals over a finite field of characteristic p, we would like to know if there exists a lift to characteristic zero with
From playlist Joint IAS/PU Number Theory Seminar
Higgs bundles and higher Teichmüller components (Lecture 1) by Oscar Garcia
DISCUSSION MEETING : MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE : 10 February 2020 to 14 February 2020 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classif
From playlist Moduli Of Bundles And Related Structures 2020
Kac polynomials and Lie algebras associated to quivers and curves – Olivier Schiffmann – ICM2018
Lie Theory and Generalizations Invited Lecture 7.1 Kac polynomials and Lie algebras associated to quivers and curves Olivier Schiffmann Abstract: We provide an explicit formula for the following enumerative problem: how many (absolutely) indecomposable vector bundles of a given rank r an
From playlist Lie Theory and Generalizations
Representations of finite groups of Lie type (Lecture 1) by Dipendra Prasad
PROGRAM : GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fun
From playlist Group Algebras, Representations And Computation
Shrawan Kumar: Root components for tensor product of affine Kac-Moody Lie algebra modules
SMRI Algebra and Geometry Online: Shrawan Kumar (University of North Carolina) Abstract: This is a joint work with Samuel Jeralds. Let 𝔤 be an affine Kac-Moody Lie algebra and let λ, µ be two dominant integral weights for 𝔤. We prove that under some mild restriction, for any positive root
From playlist SMRI Algebra and Geometry Online
This lecture is part of an online graduate course on Lie groups. This lecture is about Lie's theorem, which implies that a complex solvable Lie algebra is isomorphic to a subalgebra of the upper triangular matrices. . For the other lectures in the course see https://www.youtube.com/playl
From playlist Lie groups
On the Ramanujan Conjecture in Geometric Langlands by Dario Beraldo
Program Quantum Fields, Geometry and Representation Theory 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pandi
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)