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NPTEL

Calculus of Variations and Integral Equations

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In this course you will learn, Calculus of Variations, Integral Equations, Concepts of the calculus of variations, Variational problems with the fixed boundaries, Variational problems with moving boundaries, etc.
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40 Lesons
1 day 12 hours
On-Demand
Free-Video
NPTEL

Optimal Control, Guidance and Estimation

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Comprehensive exploration of optimal control theory, guidance systems, and estimation techniques for aerospace applications, covering LQR, dynamic programming, and Kalman filters.
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40 Lesons
1 day 15 hours
On-Demand
Free-Video
NIOS

Mathematics

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Explore advanced mathematical concepts including closed sets, matrices, calculus variations, probability, and complex analysis. Gain insights into diverse topics for a comprehensive understanding of higher mathematics.
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17 Lesons
15 hours
On-Demand
Free-Video
Ross Dynamics Lab

Principle of Least Action and Lagrange's Equations of Mechanics - Basics of Calculus of Variations

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Explore variational principles in mechanics, including the Principle of Least Action and Lagrange's equations. Learn calculus of variations techniques and their applications in physics and engineering problems.
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7 Lesons
59 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

From Frank Ramsey to René Thom: Beyond Optimization

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Explorez les problèmes d'optimisation en calcul des variations issus de la théorie économique et découvrez une nouvelle approche de solution basée sur les EDO implicites de Thom.
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1 Lesons
48 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Desigualdade Isoperimétrica - PAPMEM Janeiro 2024

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Explore a desigualdade isoperimétrica em matemática avançada. Aprofunde seus conhecimentos sobre geometria e cálculo, aprimorando suas habilidades de ensino no nível médio.
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1 Lesons
56 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Persistence in Functional Topology

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Explore functional topology's evolution, connecting persistent homology to critical point theory and calculus of variations. Gain insights into Morse's theory and its application to minimal surfaces.
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15 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Society for Industrial and Applied Mathematics

Exploring Variational Functions - Calculus of Variations and Geometric Measure Theory

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Dive into variational problems and bounded Hessian functions with Luigi Ambrosio. Explore the intersection of Calculus of Variations and Geometric Measure Theory, inspired by machine learning insights.
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1 Lesons
48 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Waists, Widths and Symplectic Embeddings

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Explore geometric measures of manifolds and their applications to symplectic embeddings. Discover area estimates for minimal submanifolds and quantitative symplectic camels in this advanced mathematics talk.
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11 Lesons
24 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Entropy and C^0 Stability of Hypersurfaces - IPAM at UCLA

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Explore entropy's role in hypersurface complexity, focusing on sphere rigidity, stability properties, and generalizations in higher dimensions. Gain insights into cutting-edge research in geometric analysis.
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10 Lesons
24 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Topological Properties of Hypersurfaces with Low Entropy - IPAM at UCLA

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Explore topological properties of hypersurfaces with low entropy, focusing on Colding-Minicozzi entropy, mean curvature flow, and closed hypersurfaces in this advanced mathematics lecture.
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8 Lesons
22 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Singularities and Diffeomorphism - IPAM at UCLA

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Explore singularities and diffeomorphism in calculus of variations, covering special cases, classification, and applications in probability and geometry.
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17 Lesons
32 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Harmonic Analysis Techniques for -Almost- Minimizers

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Explore harmonic analysis techniques for (almost-)minimizers, focusing on free boundary theory and calculus of variations. Learn about applications to geometric measure theory and domain geometry.
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12 Lesons
45 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Regularity of Free Boundaries in Obstacle Problems - Lecture III

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Explore free boundary problems in PDE, focusing on regularity of solutions and interfaces. Learn about Stefan and obstacle problems, key results, and current research challenges.
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10 Lesons
58 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Regularity of Free Boundaries in Obstacle Problems Lecture I

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Explore regularity of free boundaries in obstacle problems, covering key concepts, proofs, and current research in this mathematical field of PDE and Geometric Measure Theory.
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10 Lesons
58 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

On Yuansi Chen's Work on the KLS Conjecture III

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Explores recent progress on the KLS conjecture in high-dimensional geometry, focusing on Eldan's Stochastic Localization technique and its implications for the slicing problem.
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8 Lesons
47 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

On Yuansi Chen's Work on the KLS Conjecture I

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Explore the KLS conjecture in high-dimensional geometry, its implications for Bourgain's slicing problem, and recent progress using Eldan's Stochastic Localization technique.
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10 Lesons
46 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

On Ulam's Problem 19 and Related Problems - IPAM at UCLA

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Explore uniqueness problems related to Ulam's Problem 19 from the Scottish book, presented by Dima Ryabogin at IPAM's Calculus of Variations workshop.
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1 Lesons
26 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

On a Conjectural Symmetric Version of the Ehrhard Inequality

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Explores a conjectural symmetric version of Ehrhard's inequality for Gaussian measures, discussing minimizers, equality cases, and connections to Brascamp-Leib inequality on convex sets.
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1 Lesons
24 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Size of Line Intersections in High Dimensional L_p-Balls and Product Measures

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Explore high-dimensional geometry with Bo'az Klartag as he discusses line intersections in L_p-balls and product measures, examining the isodiametric inequality and its implications.
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1 Lesons
26 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Variational Proofs of Isoperimetric Inequalities

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Explore variational proofs of isoperimetric inequalities, their generalizations, and open problems in this advanced mathematics lecture by Steven Heilman at IPAM's workshop.
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1 Lesons
31 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Eigenvalue Estimates for P-Laplace Problems & Domains in Fermi Coordinates

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Explore explicit and sharp eigenvalue estimates for Neumann p-Laplace eigenvalues in domains represented in Fermi coordinates, presented by Barbara Brandolini at IPAM's Calculus of Variations workshop.
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1 Lesons
26 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

On Yuansi Chen's Work on the KLS Conjecture II

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Explores recent progress on the KLS conjecture in high-dimensional geometry, focusing on Yuansi Chen's work and Eldan's Stochastic Localization technique. Discusses implications for Bourgain's slicing problem.
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1 Lesons
46 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Regularity of Free Boundaries in Obstacle Problems - Lecture IV

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Explore advanced concepts in free boundary problems, focusing on regularity in obstacle problems. Learn key results, current research, and open challenges in this mathematical field.
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1 Lesons
54 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Regularity of Free Boundaries in Obstacle Problems - Lecture II

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Explore free boundary problems in PDE, focusing on regularity in obstacle problems. Learn key results, current research, and open questions in this mathematical field.
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1 Lesons
56 minutes
On-Demand
Free-Video
ICTP Mathematics

Regularity Theory for Area-Minimizing Currents - Lecture 5

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Explore advanced concepts in geometric measure theory, focusing on regularity theory for area-minimizing currents. Gain insights from experts De Lellis and Spadaro in this in-depth lecture.
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1 Lesons
1 hour 49 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 25

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and their applications in various scientific fields.
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1 Lesons
1 hour 35 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 28

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and their applications in various scientific fields.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 24

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and their applications in this comprehensive lecture.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 21

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and problem-solving techniques in this comprehensive lecture.
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1 Lesons
1 hour 23 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 13

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and problem-solving techniques in this comprehensive lecture.
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1 Lesons
1 hour 36 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 8

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and problem-solving techniques in this comprehensive lecture.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Isoperimetric Problem- From Classical to Reverse I

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Explore the classical isoperimetric problem and its reverse, focusing on minimizing volume for convex bodies with bounded curvature. Learn about recent developments in R3.
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1 Lesons
53 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Isoperimetric Problem- From Classical to Reverse II

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Explore the reverse isoperimetric problem for convex bodies with bounded curvature, focusing on volume minimization in R3 and its implications for geometric analysis.
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1 Lesons
50 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Isoperimetric Problem - From Classical to Reverse III

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Explores the reverse isoperimetric problem for convex bodies with bounded curvature, focusing on volume minimization in R3 and its implications for geometric analysis.
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1 Lesons
51 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Vysotskiy - The Isoperimetric Problem for Convex Hulls and the Large Deviations Rate Functions

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Explores large deviations principle for convex hull areas in planar random walks, analyzing optimal trajectories and solving the Euler-Lagrange equation for various rate functions.
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1 Lesons
28 minutes
On-Demand
Free-Video
Fields Institute

Boundary Regularity of Minimal Surfaces

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Explore boundary regularity of minimal surfaces with Camillo De Lellis. Gain insights into advanced mathematical concepts and their applications in geometric analysis.
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1 Lesons
42 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Progressive Decoupling of Dynamics in Convex Optimal Control

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Explore progressive decoupling in convex optimization for optimal control, connecting classical calculus of variations with modern convex analysis and duality concepts.
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1 Lesons
34 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Antagonistic Cost Functionals in Shape Optimization

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Explore antagonistic cost functionals in shape optimization with Giuseppe Buttazzo, delving into new perspectives and advanced mathematical concepts.
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1 Lesons
45 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Variational Theory for Harmonic Maps and Applications - Lecture 1

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Explore variational theory for harmonic maps and its applications in this advanced mathematical lecture by Daniel Stern.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Variational Theory for Harmonic Maps and Applications - Lecture 2

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Explore advanced variational theory for harmonic maps and its applications in geometric analysis through this in-depth mathematical lecture.
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1 Lesons
1 hour 25 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Nash's C^1 Isometric Embedding Theorem and the Borisov-Gromov Problem - Lecture 3

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Explore Nash's C^1 isometric embedding theorem and the Borisov-Gromov problem in Riemannian geometry. Delve into surprising constructions and open questions linked to the Onsager conjecture.
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1 Lesons
1 hour 53 minutes
On-Demand
Free-Video
Institute for Advanced Study

The Isoperimetric Problem in Cubes and Torii

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Explore the isoperimetric problem in cubes and torii, delving into geometric principles and mathematical concepts with Federico Glaudo's insightful analysis.
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1 Lesons
23 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Symmetries, Conservation Laws and Variational Principles - Part III

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Explore symmetries, conservation laws, and variational principles in mathematics, focusing on Noether Theorems and their applications in various geometric structures and physical systems.
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10 Lesons
1 hour 15 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Symmetries, Conservation Laws and Variational Principles - Part II

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Explore advanced mathematics of Noether Theorems in calculus of variations, covering symmetries, conservation laws, and variational principles. Gain insights into differential geometric structures and their applications.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Symmetries, Conservation Laws and Variational Principles

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Explore symmetries, conservation laws, and variational principles in mathematics, focusing on Noether Theorems and their applications in calculus of variations and differential geometry.
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1 Lesons
54 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Generic Regularity in Obstacle Problems

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Explore the classical obstacle problem, its free boundary, and recent developments in regularity theory with insights from renowned mathematician Alessio Figalli.
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1 Lesons
47 minutes
On-Demand
Free-Video
Banach Center

Geometric Aspects of the Planar Least Gradient Problem

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Explore geometric aspects of the planar least gradient problem, delving into mathematical concepts and analytical techniques.
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1 Lesons
41 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Riesz Inequality for Polygons: Symmetry and Symmetry Breaking

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Explore counterparts of Hardy-Littlewood and Riesz inequalities for polygons, examining symmetry and symmetry breaking in nonlocal isoperimetric problems.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Eigenvalues and Minimal Surfaces

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Explore Laplace operator eigenvalues, their physical significance, and connection to minimal surfaces. Discover recent findings in isoperimetric eigenvalue problems for Riemannian surfaces.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
BIMSA

Optimal Immersions in the Calculus of Variations of Surfaces

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Explore innovative minmax techniques for optimal surface immersions, including recent progress on Yau, Willmore, and 16π conjectures in calculus of variations.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Institute for Advanced Study

Regularity for Stationary Varifolds

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Explore advanced concepts in geometric measure theory, focusing on regularity properties of stationary varifolds and their applications in minimal surface theory.
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1 Lesons
20 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Dissipation and Mixing: From Turbulent Flows to Weak Solutions - Lecture 1

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Explore dissipation and mixing in turbulent flows, focusing on weak solutions in hydrodynamics. Gain insights into anomalous dissipation and recent developments in mathematical fluid mechanics.
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1 Lesons
1 hour 57 minutes
On-Demand
Free-Video
Dot Physics

Solving the Brachistochrone Problem with Random Numbers

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Discover the fastest path for a frictionless bead using random numbers to solve the Brachistochrone problem in physics.
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1 Lesons
20 minutes
On-Demand
Free-Video
Dot Physics

Review of Lagrangian Mechanics with Examples - Projectile Motion and Driven Spring Oscillation

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Explore Lagrangian mechanics through projectile motion and driven spring oscillation examples, including numerical calculations and Python implementation.
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5 Lesons
29 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

C^0 Convex Integration for Incompressible Euler - Lecture 4

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Explore C^0 convex integration for incompressible Euler equations, focusing on a novel iteration method producing continuous solutions, drawing parallels with Nash's theorem from Lecture 3.
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1 Lesons
2 hours 3 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

The Brownian Transport Map - IPAM at UCLA

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Explore Lipschitz transport maps between probability measures, focusing on the Brownian transport map's construction, properties, and applications to Euclidean functional inequalities.
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10 Lesons
24 minutes
On-Demand
Free-Video
ICTP Mathematics

Introduction to Optimal Transportation and Monge Ampère Type Equations - Lecture 2

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Explore optimal transportation and Monge Ampère equations, covering key concepts like super differentials, isoperimetric problems, and probability measures in this advanced mathematics lecture.
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15 Lesons
1 hour 58 minutes
On-Demand
Free-Video
Conference GSI

A Variational Principle of Minimum for Navier-Stokes Equation Based on the Symplectic Formalism

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Explore a variational principle of minimum for Navier-Stokes equations using symplectic formalism, advancing understanding of fluid dynamics and mathematical physics.
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1 Lesons
24 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Patterns in Tri-Block Copolymers: Droplets, Double-Bubbles and Core-Shells - A New Partitioning Problem

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Explore patterns in tri-block copolymers, including droplets, double-bubbles, and core-shells. Examine a novel partitioning problem in mathematical physics and materials science.
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1 Lesons
53 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Variational Principles in Physics - Standard Prejudices and Paradoxes

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Explore variational principles in physics, challenging standard assumptions and uncovering paradoxes with Professor Jerzy Kijowski's insightful seminar.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Onsager Theorem and Beyond - Lecture Series

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Explore advanced topics in fluid dynamics and differential geometry with renowned mathematician Camillo De Lellis, covering Onsager's theorem, Euler equations, and isometric embeddings.
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5 Lesons
1 hour 37 minutes
On-Demand
Free-Video
Dot Physics

Classical Mechanics - Introduction to Lagrangian Mechanics

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Explore the fundamental principles of Lagrangian mechanics, a powerful mathematical framework for analyzing physical systems and understanding classical mechanics.
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1 Lesons
24 minutes
On-Demand
Free-Video