Lie groups | Complex manifolds | Homogeneous spaces | Differential geometry | Riemannian geometry
In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has an inversion symmetry preserving the Hermitian structure. First studied by Élie Cartan, they form a natural generalization of the notion of Riemannian symmetric space from real manifolds to complex manifolds. Every Hermitian symmetric space is a homogeneous space for its isometry group and has a unique decomposition as a product of irreducible spaces and a Euclidean space. The irreducible spaces arise in pairs as a non-compact space that, as Borel showed, can be embedded as an open subspace of its compact dual space. Harish Chandra showed that each non-compact space can be realized as a bounded symmetric domain in a complex vector space. The simplest case involves the groups SU(2), SU(1,1) and their common complexification SL(2,C). In this case the non-compact space is the unit disk, a homogeneous space for SU(1,1). It is a bounded domain in the complex plane C. The one-point compactification of C, the Riemann sphere, is the dual space, a homogeneous space for SU(2) and SL(2,C). Irreducible compact Hermitian symmetric spaces are exactly the homogeneous spaces of simple compact Lie groups by maximal closed connected subgroups which contain a maximal torus and have center isomorphic to the circle group. There is a complete classification of irreducible spaces, with four classical series, studied by Cartan, and two exceptional cases; the classification can be deduced from Borel–de Siebenthal theory, which classifies closed connected subgroups containing a maximal torus. Hermitian symmetric spaces appear in the theory of Jordan triple systems, several complex variables, complex geometry, automorphic forms and group representations, in particular permitting the construction of the holomorphic discrete series representations of semisimple Lie groups. (Wikipedia).
Hermitian Operators (Self-Adjoint Operators) | Quantum Mechanics
In this video, we will talk about Hermitian operators in quantum mechanics. If an operator A is a Hermitian operator, then it is the same as its adjoint operator A-dagger, which is defined via this equation here. Usually, the terms "Hermitian" and "self adjoint" are used interchangeably, h
From playlist Quantum Mechanics, Quantum Field Theory
Math 060 Fall 2017 112717C Hermitian Matrices Part 1
Definitions: complex conjugate, modulus, complex vector, conjugate transpose, complex inner product, conjugate matrix. Hermitian matrices. Hermitian matrices and the inner product. Hermitian matrices have 1. real eigenvalues, 2. orthogonal eigenspaces. Unitary matrices. Hermitian matr
From playlist Course 4: Linear Algebra (Fall 2017)
The Geometry of Quantum States by Chia-Yi Ju
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
From playlist Non-Hermitian Physics (ONLINE)
Non-Hermitian Disorder: Spectra, Localization, Dynamics by K. G. Makris
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
From playlist Non-Hermitian Physics (ONLINE)
Non-Equilibrium Steady States of Quantum Non-Hermitian Lattice Models by Aashish Clerk
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
From playlist Non-Hermitian Physics (ONLINE)
A WEIRD VECTOR SPACE: Building a Vector Space with Symmetry | Nathan Dalaklis
We'll spend time in this video on a weird vector space that can be built by developing the ideas around symmetry. In the process of building a vector space with symmetry at its core, we'll go through a ton of different ideas across a handful of mathematical fields. Naturally, we will start
From playlist The New CHALKboard
Yonatan Harpaz - New perspectives in hermitian K-theory I
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory
Simulating Non-Hermitian Dynamics of a Multi-Spin Quantum System by Anant Vijay Varma
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
From playlist Non-Hermitian Physics (ONLINE)
Coherent State Structure of Pseudo-Hermitian Hamiltonian Systems....by Pinaki Patra
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
From playlist Non-Hermitian Physics (ONLINE)
Exceptional Points in Closed Quantum Systems by Miloslav Znojil
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
From playlist Non-Hermitian Physics (ONLINE)
Unmasking PT Symmetry by Carl M. Bender
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
From playlist Non-Hermitian Physics (ONLINE)
L24.1 Symmetrizer and antisymmetrizer for N particles
MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L24.1 Symmetrizer and antisymmetrizer for N particles License: Creative
From playlist MIT 8.06 Quantum Physics III, Spring 2018
Lie Groups and Lie Algebras: Lesson 11 - The Classical Groups Part IX
Lie Groups and Lie Algebras: Lesson 11 - The Classical Groups Part IX In this lecture we count the degrees of freedom for the classical groups. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
PT phase transition in non-abelian system by Haresh Raval
Non-Hermitian Physics - PHHQP XVIII DATE: 04 June 2018 to 13 June 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore Non-Hermitian Physics-"Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP) XVIII" is the 18th meeting in the series that is being held over the years in Quantum Phys
From playlist Non-Hermitian Physics - PHHQP XVIII
Quantum-classical Correspondence in Chaotic PT-symmetric Systems by Eva-Maria Graefe
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
From playlist Non-Hermitian Physics (ONLINE)
Determinantal varieties and asymptotic expansion of Bergman kernels by Harald Upmeier
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
Non-Hermiticity: A New Paradigm for Model Building in Particle Physics by Peter Millington
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
From playlist Non-Hermitian Physics (ONLINE)
Dror Varolin - Minicourse - Lecture 1
Dror Varolin Variations of Holomorphic Hilbert spaces Traditional complex analysis focuses on a single space, like a domain in Euclidean space, or more generally a complex manifold, and studies holomorphic maps on that space, into some target space. The typical target space for a domain i
From playlist Maryland Analysis and Geometry Atelier
Dynamical Phases and Quantum Correlations in an Emitter-Waveguide System... by Beatriz Olmos-Sanchez
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
From playlist Non-Hermitian Physics (ONLINE)