Calculus of variations | Optimal control
The Beltrami identity, named after Eugenio Beltrami, is a special case of the Euler–Lagrange equation in the calculus of variations. The Euler–Lagrange equation serves to extremize action functionals of the form where and are constants and . If , then the Euler–Lagrange equation reduces to the Beltrami identity, where C is a constant. (Wikipedia).
Wild Weak Solutions to Equations arising in Hydrodynamics - 2/6 - Vlad Vicol
In this course, we will discuss the use of convex integration to construct wild weak solutions in the context of the Euler and Navier-Stokes equations. In particular, we will outline the resolution of Onsager's conjecture as well as the recent proof of non-uniqueness of weak solutions to t
From playlist Hadamard Lectures 2020 - Vlad Vicol and - Wild Weak Solutions to Equations arising in Hydrodynamics
The Beltrami Identity is a necessary condition for the Euler-Lagrange equation (so if it solves the E-L equation, it solves the Beltrami identity). Here it is derived from the total derivative of the integrand (e.g. Lagrangian).
From playlist Physics
Yilin Wang - 4/4 The Loewner Energy at the Crossroad of Random Conformal Geometry (...)
The Loewner energy for Jordan curves first arises from the large deviations of Schramm-Loewner evolution (SLE), a family of random fractal curves modeling interfaces in 2D statistical mechanics. In a certain way, this energy measures the roundness of a Jordan curve, and we show that it is
From playlist Yilin Wang - The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory
The many facets of complexity of Beltrami fields in Euclidean space - Daniel Peralta-Salas
Workshop on the h-principle and beyond Topic: The many facets of complexity of Beltrami fields in Euclidean space Speaker: Daniel Peralta-Salas Affiliation: Instituto de Ciencias Matemáticas Date: November 02, 2021 Beltrami fields, that is vector fields on $\mathbb R^3$ whose curl is p
From playlist Mathematics
Illuminating hyperbolic geometry
Joint work with Saul Schleimer. In this short video we show how various models of hyperbolic geometry can be obtained from the hemisphere model via stereographic and orthogonal projection. 2D figure credits: 4:09 Cannon, Floyd, Kenyon, Parry. 0:49, 1:20, 1:31, 2:12, Roice Nelson. We th
From playlist 3D printing
Looking at Euler flows through a contact mirror: Universality, Turing… - Eva Miranda
Workshop on the h-principle and beyond Topic: Looking at Euler flows through a contact mirror: Universality, Turing completeness and undecidability Speaker: Eva Miranda Affiliation: Universitat Politècnica de Catalunya Date: November 1, 2021 The dynamics of an inviscid and incompressible
From playlist Mathematics
Lecture 18: The Laplace Operator (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Harmonic Maps between surfaces and Teichmuller theory (Lecture - 2) by Michael Wolf
Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b
From playlist Geometry, Groups and Dynamics (GGD) - 2017
8ECM Invited Lecture: Eva Miranda
From playlist 8ECM Invited Lectures
C. Leininger - Teichmüller spaces and pseudo-Anosov homeomorphism (Part 2)
I will start by describing the Teichmuller space of a surface of finite type from the perspective of both hyperbolic and complex structures and the action of the mapping class group on it. Then I will describe Thurston's compactification of Teichmuller space, and state his classification t
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
