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
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
The adjoint Brascamp-Lieb inequality - Terence Tao
Analysis and Mathematical Physics Topic: The adjoint Brascamp-Lieb inequality Speaker: Terence Tao Affiliation: University of California, Los Angeles Date: March 08, 2023 The Brascamp-Lieb inequality is a fundamental inequality in analysis, generalizing more classical inequalities such a
From playlist Mathematics
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
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
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
Haonan Zhang: "How far can we go with Lieb's concavity theorem and Ando's convexity theorem?"
Entropy Inequalities, Quantum Information and Quantum Physics 2021 "How far can we go with Lieb's concavity theorem and Ando's convexity theorem?" Haonan Zhang - Institute of Science and Technology Austria (IST Austria) Abstract: In a celebrated paper in 1973, Lieb proved what we now cal
From playlist Entropy Inequalities, Quantum Information and Quantum Physics 2021
Virginie Ehrlacher - Sparse approximation of the Lieb functional in DFT with moment constraints
Recorded 28 March 2023. Virginie Ehrlacher of the École Nationale des Ponts-et-Chaussées presents "Sparse approximation of the Lieb functional in DFT with moment constraints (joint work with Luca Nenna)" at IPAM's Increasing the Length, Time, and Accuracy of Materials Modeling Using Exasca
From playlist 2023 Increasing the Length, Time, and Accuracy of Materials Modeling Using Exascale Computing
This lecture is part of an online graduate course on Lie groups. We give an introductory survey of Lie groups theory by describing some examples of Lie groups in low dimensions. Some recommended books: Lie algebras and Lie groups by Serre (anything by Serre is well worth reading) Repre
From playlist Lie groups
Liquid crystals and interacting dimer models - Ian Jauslin
Short talks by postdoctoral members Topic: Liquid crystals and interacting dimer models Speaker: Ian Jauslin Affiliation: Member, School of Mathematics Date: September 29, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Coordinate Scaling Constraints in Density and Density- Matrix Functional Theories
Mel Levy, Tulane University, USA
From playlist Distinguished Visitors Lecture Series
2020.07.02 Ron Peled - Fluctuations of random surfaces and concentration inequalities
Random surfaces in statistical physics are commonly modeled by a real-valued function on a d-dimensional lattice, whose probability density penalizes nearest-neighbor fluctuations according to an interaction potential U. The case U(x)=x^2 is the well-studied lattice Gaussian free field, wh
From playlist One World Probability Seminar
Robert Seiringer: The local density approximation in density functional theory
We present a mathematically rigorous justification of the Local Density Approximation in density functional theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density (the lowest possible energy of all quantum st
From playlist Mathematical Physics
Frank Morgan: Isoperimetry with density
Abstract : In 2015 Chambers proved the Log-convex Density Conjecture, which says that for a radial density f on Rn, spheres about the origin are isoperimetric if and only if log f is convex (the stability condition). We discuss recent progress and open questions for other densities, unequa
From playlist Control Theory and Optimization
Proof of a 35 Year Old Conjecture for Entropy of Coherent States and Generalization - Elliot Lieb
Elliot Lieb Princeton University November 12, 2012 35 years ago Wehrl defined a classical entropy of a quantum density matrix using Gaussian (Schr\"odinger, Bargmann, ...) coherent states. This entropy, unlike other classical approximations, has the virtue of being positive. He conjectured
From playlist Mathematics
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
Volker Bach - The Hartree-Fock Approximation and its Generalizations - IPAM at UCLA
Recorded 11 April 2022. Volker Bach of TU Braunschweig presents "The Hartree-Fock Approximation and its Generalizations" at IPAM's Model Reduction in Quantum Mechanics Workshop. Abstract: In the talk the Hartree-Fock (HF) approximation in quantum mechanics will be reviewed. The following p
From playlist 2022 Model Reduction in Quantum Mechanics Workshop
Liquid Crystals and the Heilmann-Lieb Conjecture - Ian Jauslin
https://www.ias.edu/events/friends-lunch-member-jauslin More videos on http://video.ias.edu
From playlist Friends of the Institute
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
Mathieu Lewin - Recent results in Density Functional Theory - IPAM at UCLA
Recorded 12 April 2022. Mathieu Lewin of CNRS and Université Paris-Dauphine presents "Recent results in Density Functional Theory" at IPAM's Model Reduction in Quantum Mechanics Workshop. Abstract: I will provide an overview of results obtained recently in density functional theory, in joi
From playlist 2022 Model Reduction in Quantum Mechanics Workshop