In the calculus of variations, a branch of mathematics, a Nehari manifold is a manifold of functions, whose definition is motivated by the work of Zeev Nehari . It is a differentiable manifold associated to the Dirichlet problem for the semilinear elliptic partial differential equation Here Δ is the Laplacian on a bounded domain Ω in Rn. There are infinitely many solutions to this problem. Solutions are precisely the critical points for the energy functional on the Sobolev space H10(Ω). The Nehari manifold is defined to be the set of v ∈ H10(Ω) such that Solutions to the original variational problem that lie in the Nehari manifold are (constrained) minimizers of the energy, and so direct methods in the calculus of variations can be brought to bear. More generally, given a suitable functional J, the associated Nehari manifold is defined as the set of functions u in an appropriate function space for which Here J′ is the functional derivative of J. (Wikipedia).
Manifolds 1.3 : More Examples (Animation Included)
In this video, I introduce the manifolds of product manifolds, tori/the torus, real vectorspaces, matrices, and linear map spaces. This video uses a math animation for visualization. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/5koj5
From playlist Manifolds
Ancient Egyptian Flute Ney music
A piece for Egyptian Ney flute inspired by Percy Bysshe Shelley's poem "Ozymandias". https://bit.ly/2ORgICI (picture from Tomb of Mehu at Saqqara, Sixth Dynasty, 2300 BC.) A reed flute Ney is believed to be the most ancient musical instrument played up to this day. It dates back to pred
From playlist Music
Schwarzian derivatives and Epstein surfaces (Lecture 02) by Ken Bromberg
DISCUSSION MEETING SURFACE GROUP REPRESENTATIONS AND PROJECTIVE STRUCTURES ORGANIZERS: Krishnendu Gongopadhyay, Subhojoy Gupta, Francois Labourie, Mahan Mj and Pranab Sardar DATE: 10 December 2018 to 21 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore The study of spaces o
From playlist Surface group representations and Projective Structures (2018)
Manifolds 1.1 : Basic Definitions
In this video, I give the basic intuition and definitions of manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
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What is a Manifold? Lesson 6: Topological Manifolds
Topological manifolds! Finally! I had two false starts with this lesson, but now it is fine, I think.
From playlist What is a Manifold?
#Mandala MANDALA LOVERS ALERT- Mandala (Sanskrit: मण्डल, lit, circle) is a spiritual and ritual symbol in Indian religions, representing the universe-check out more videos about mandala below-. * check out my Blog Post for details on Mandala supplies- https://www.theartgeekblog.com/post/mu
From playlist Bag
Manifolds 1.2 : Examples of Manifolds
In this video, I describe basic examples of manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/IZO0G25
From playlist Manifolds
Manifolds 1.5 : Manifolds with Boundary (Animation Included)
CORRECTION : https://youtu.be/quqk2X_zvB8 In this video, I introduce manifolds with boundary, including the famous Mobius Strip. This video uses a math animation for visualization. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet Playlist :
From playlist Manifolds
Haim Sompolinsky: "Statistical Mechanics of Deep Manifolds: Mean Field Geometry in High Dimension"
Machine Learning for Physics and the Physics of Learning 2019 Workshop IV: Using Physical Insights for Machine Learning "Statistical Mechanics of Deep Manifolds: Mean Field Geometry in High Dimension" Haim Sompolinsky - The Hebrew University of Jerusalem Abstract: Recent advances in sys
From playlist Machine Learning for Physics and the Physics of Learning 2019
Fitting a manifold to noisy data by Hariharan Narayanan
DISCUSSION MEETING THE THEORETICAL BASIS OF MACHINE LEARNING (ML) ORGANIZERS: Chiranjib Bhattacharya, Sunita Sarawagi, Ravi Sundaram and SVN Vishwanathan DATE : 27 December 2018 to 29 December 2018 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore ML (Machine Learning) has enjoyed tr
From playlist The Theoretical Basis of Machine Learning 2018 (ML)
Rustam Sadykov (1/28/21): On the Lusternik-Schnirelmann theory of 4-manifolds
Title: On the Lusternik-Schnirelmann theory of 4-manifolds Abstract: I will discuss various versions of the Lusternik-Schnirelman category involving covers and fillings of 4-manifolds by various sets. In particular, I will discuss Gay-Kirby trisections, which are certain decompositions o
From playlist Topological Complexity Seminar
Jintian Zhu - Incompressible hypersurface, positive scalar curvature and positive mass theorem
In this talk, I will introduce a positive mass theorem for asymptotically flat manifolds with fibers (like ALF and ALG manifolds) under an additional but necessary incompressible condition. I will also make a discussion on its connection with surgery theory as well as quasi-local mass and
From playlist Not Only Scalar Curvature Seminar
Fitting manifolds to data - Charlie Fefferman
Workshop on Topology: Identifying Order in Complex Systems Topic: Fitting manifolds to data Speaker: Charlie Fefferman Affiliation: Princeton University Date: April 7, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Brent Pym: Holomorphic Poisson structures - lecture 3
The notion of a Poisson manifold originated in mathematical physics, where it is used to describe the equations of motion of classical mechanical systems, but it is nowadays connected with many different parts of mathematics. A key feature of any Poisson manifold is that it carries a cano
From playlist Virtual Conference
Hao Xu (7/26/22): Frobenius algebra structure of statistical manifold
Abstract: In information geometry, a statistical manifold is a Riemannian manifold (M,g) equipped with a totally symmetric (0,3)-tensor. We show that the tangent bundle of a statistical manifold has a Frobenius algebra structure if and only if the sectional K-curvature vanishes. This gives
From playlist Applied Geometry for Data Sciences 2022
Winter School JTP: Introduction to Fukaya categories, James Pascaleff, Lecture 1
This minicourse will provide an introduction to Fukaya categories. I will assume that participants are also attending Keller’s course on A∞ categories. Lecture 1: Basics of symplectic geometry for Fukaya categories. Symplectic manifolds; Lagrangian submanifolds; exactness conditions;
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
Noémie Combe - How many Frobenius manifolds are there?
In this talk an overview of my recent results is presented. In a joint work with Yu. Manin (2020) we discovered that an object central to information geometry: statistical manifolds (related to exponential families) have an F-manifold structure. This algebraic structure is a more general v
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Nemaliki nerpina nadakalivi_Saptapadi
From playlist Telugu Songs