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 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
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
Schemes 46: Differential operators
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we define differential operators on rings, and calculate the universal (normalized) differential operator of order n. As a special case we fin
From playlist Algebraic geometry II: Schemes
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
The Weyl algebra and the Heisenberg Lie algebra
In this video we give a simple teaser into the world of operator algebras. In particular, we talk about the Weyl algebra and compute some expressions that fulfill the property which defines the Heisenberg Lie algebra http://math.uchicago.edu/~may/REU2012/REUPapers/Lingle.pdf https://en.w
From playlist Algebra
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined In this lecture we define a "continuous groups" and show the connection between the algebraic properties of a group with topological properties. Please consider supporting this channel via Patreon: https://www.patreon.co
From playlist Lie Groups and Lie Algebras
Jean Michel BISMUT - Fokker-Planck Operators and the Center of the Enveloping Algebra
The heat equation method in index theory gives an explicit local formula for the index of a Dirac operator. Its Lagrangian counterpart involves supersymmetric path integrals. Similar methods can be developed to give a geometric formula for semi simple orbital integrals associated with the
From playlist Integrability, Anomalies and Quantum Field Theory
Lie groups: Lie groups and Lie algebras
This lecture is part of an online graduate course on Lie groups. We discuss the relation between Lie groups and Lie algebras, and give several examples showing how they behave differently. Lie algebras turn out to correspond more closely to the simply connected Lie groups. We then explain
From playlist Lie groups
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
Lie Groups and Lie Algebras: Lesson 18- Group Generators
Lie Groups and Lie Algebras: Lesson 18- Generators This is an important lecture! We work through the calculus of *group generators* and walk step-by-step through the exploitation of analyticity. That is, we use the Taylor expansion of the continuous functions associated with a Lie group o
From playlist Lie Groups and Lie Algebras
Duality between estimation and control - Sanjoy Mitter
PROGRAM: Data Assimilation Research Program Venue: Centre for Applicable Mathematics-TIFR and Indian Institute of Science Dates: 04 - 23 July, 2011 DESCRIPTION: Data assimilation (DA) is a powerful and versatile method for combining observational data of a system with its dynamical mod
From playlist Data Assimilation Research Program
Stokes phenomena, Poisson-Lie groups and quantum groups - Valerio Toledano Laredo
Workshop on Representation Theory and Geometry Topic: Stokes phenomena, Poisson-Lie groups and quantum groups Speaker: Valerio Toledano Laredo Affiliation: Northeastern University; Member, School of Mathematics Date: April 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Mod-01 Lec-19 Linear Least Square Estimation and Geometric Interpretation
Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Bombay: Advanced Numerical Analysis | CosmoLearning.org
Tony Yue Yu - 2/4 The Frobenius Structure Conjecture for Log Calabi-Yau Varieties
Notes: https://nextcloud.ihes.fr/index.php/s/8KTr2Mfdk22rpqX 2/4 - Skeletal curves: a key notion in the theory. --- We show that the naive counts of rational curves in an affine log Calabi-Yau variety U, containing an open algebraic torus, determine in a surprisingly simple way, a family
From playlist Tony Yue Yu - The Frobenius Structure Conjecture for Log Calabi-Yau Varieties
Lie Groups for Deep Learning w/ Graph Neural Networks
Lie Groups encode the symmetry of systems. We examine actions of a Lie group on a vector space, given their algebraic, topological and analysis based connectome. Deep Learning algorithms for Graph Neural Networks (GNN) are non trivial, and to understand them Lie Groups are essential! A r
From playlist Learn Graph Neural Networks: code, examples and theory
Julien Grivaux - The Lie algebra attached to a tame closed embedding
Abstract: If X is a smooth closed subscheme of an ambient smooth scheme Y, Calaque, Caldararu and Tu have endowed the shifted normal bundle NX/Y[−1] with a derived Lie algebroid structure. This structure generalizes the Lie algebra structure on the shifted tangent bundle TX[−1] on a smoot
From playlist Algebraic Analysis in honor of Masaki Kashiwara's 70th birthday
Linear Algebra 5.4 Differential Equations
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul A. Roberts is supported in part by the grants NSF CAREER 1653602 and NSF DMS 2153803.
From playlist Linear Algebra
Measures on spaces of Riemannian metrics - Dmitry Jakobson
Dmitry Jakobson McGill University July 21, 2014 This is joint work with Y. Canzani, B. Clarke, N. Kamran, L. Silberman and J. Taylor. We construct Gaussian measure on the manifold of Riemannian metrics with the fixed volume form. We show that diameter and Laplace eigenvalue and volume entr
From playlist Mathematics