Lie derivatives of differential forms
Introduces the lie derivative, and its action on differential forms. This is applied to symplectic geometry, with proof that the lie derivative of the symplectic form along a Hamiltonian vector field is zero. This is really an application of the wonderfully named "Cartan's magic formula"
From playlist Symplectic geometry and mechanics
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
Lie derivative of a vector field (flow and pushforward)
Part 2: https://youtu.be/roFNj3k4Lmc In this video I show you how you can derive the Lie derivative of a vector field. First, we look at a vector field on a manifold and develop the notion of an integral curve followed by the flow of the vector field. We can then move another vector along
From playlist Lie derivative
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
Lie Groups and Lie Algebras: Lesson 7 - The Classical Groups Part V
Lie Groups and Lie Algebras: Lesson 7 - The Classical Groups Part V We discuss the matrix interpretation of the metric even more, since it is critical to our understanding of the classical groups. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
Lie Groups and Lie Algebras: Lesson 3 - Classical Groups Part I
Lie Groups and Lie Algebras: Lesson 3 - Classical Groups Part I We introduce the idea of the classical matrix groups and their associated carrier spaces. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
Lie Groups and Lie Algebras:Lesson 24: Putting Matrix Group Generators to work.
Lie Groups and Lie Algebras:Lesson 24: Putting Matrix Group Generators to work. In this lesson we examine the vector space formed by the groups generators ands how all the members of that vector space are also group generators. We take not that this vector space is not yet a "algebra" be
From playlist Lie Groups and Lie Algebras
Lie derivative pt. 2: Properties and general tensors
Part 1: https://youtu.be/vFsqbsRl_K0 Updated version with the sign error fixed (sort of). The previous version of this video contained an ugly sign error as pointed out by Magist. It should now be clear what the correct sign is. Unfortunately, I also had to cut out part of the video becau
From playlist Lie derivative
Pavel Etingof: Poisson-Lie groups and Lie bialgebras - Lecture 2
HYBRID EVENT Recorded during the meeting "Lie Theory and Poisson Geometry" the January 11, 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 Audiov
From playlist Virtual Conference
This lecture is part of an online graduate course on Lie groups. We state Engel's theorem about nilpotent Lie algebras and sketch a proof of it. We give an example of a nilpotent Lie group that is not a matrix group. For the other lectures in the course see https://www.youtube.com/play
From playlist Lie groups
Lie groups: Poincare-Birkhoff-Witt theorem
This lecture is part of an online graduate course on Lie groups. We state the Poincare-Birkhoff Witt theorem, which shows that the universal enveloping algebra (UEA) of a Lie algebra is the same size as a polynomial algebra. We prove it for Lie algebras of Lie groups and sketch a proof of
From playlist Lie groups
Vector Calculus 17: The Derivative of a Vector Function Is the Tangent to the Curve
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 Vector Calculus
Verlinde Dimension Formula for the Space of Conformal Blocks and the moduli of G...V- Shrawan Kumar
Verlinde Dimension Formula Topic: Verlinde Dimension Formula for the Space of Conformal Blocks and the moduli of G-bundles V Speaker: Shrawan Kumar Affiliation: University of North Carolina; Member, School of Mathematics Date: November 17, 2022 Let G be a simply-connected complex semisim
From playlist Mathematics
Title: Rational Matrix Differential Operators and Integral Systems of PDEs
From playlist Fall 2017
Is the variety of singular tuples of matrices a null cone? - Viswambhara Makam
Computer Science/Discrete Mathematics Seminar II Topic: Is the variety of singular tuples of matrices a null cone? - Speaker: Viswambhara Makam Affiliation: Member, School of Mathematics Date: February 25, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Lie algebras with @TomRocksMaths
Teaching Tom Crawford a bit about my favorite subject -- Lie algebras. Check out Part 2: https://www.youtube.com/watch?v=ap7GZKCcgS8 🌟Support the channel🌟 Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.am
From playlist Collaborations
Nigel Hitchin "Higgs bundles, past and present" [2012]
2012 FIELDS MEDAL SYMPOSIUM Thursday, October 18 Geometric Langlands Program and Mathematical Physics Nigel Hitchin, Oxford University Higgs bundles, past and present The talk will be an overview of the moduli spaces of Higgs bundles, or equivalently solutions to the so-called Hitchin eq
From playlist Number Theory
After our introduction to matrices and vectors and our first deeper dive into matrices, it is time for us to start the deeper dive into vectors. Vector spaces can be vectors, matrices, and even function. In this video I talk about vector spaces, subspaces, and the porperties of vector sp
From playlist Introducing linear algebra
Lie Groups and Lie Algebras: Lesson 5 - The Classical Groups Part III
Lie Groups and Lie Algebras: Lesson 5 - The Classical Groups Part III We consider the notion of a transformation that preserves the structure of a metric and show that the set of such transformations is a group. Please consider supporting this channel via Patreon: https://www.patreon.co
From playlist Lie Groups and Lie Algebras