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#Variational Methods

Showing: 45 courses
Centre de recherches mathématiques - CRM

Sharp Stability of Higher Order Dirichlet Eigenvalues

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Explorez la stabilité des valeurs propres de Dirichlet d'ordre supérieur, en examinant les limites nettes pour les valeurs propres dégénérées et les groupes de valeurs propres.
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17 Lesons
51 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

A Variational Method for Functionals Depending on Eigenvalues

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Explore a new variational method for optimizing eigenvalue-dependent functionals in spectral geometry, simplifying and unifying previous results in 2D and extending to higher dimensions.
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1 Lesons
51 minutes
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Free-Video
Centre International de Rencontres Mathématiques

An Implicit Formulation for Incorporating Different Priors into a Deformation Model

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Explore an implicit formulation for incorporating diverse priors into deformation models, enhancing geometric analysis and shape modeling techniques.
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1 Lesons
38 minutes
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Free-Video
NPTEL-NOC IITM

Introduction to the Finite Element Method - Basic Framework of FEM

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Explore the fundamental concepts and framework of the Finite Element Method (FEM) in this introductory video lecture.
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1 Lesons
25 minutes
On-Demand
Free-Video
International Mathematical Union

Modern Regularization Methods in Inverse Problems and Data Science

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Explores recent developments in variational methods for inverse problems and machine learning, discussing convergent regularization schemes, quantitative estimates, and connections between classical regularization theory and risk minimization.
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1 Lesons
45 minutes
On-Demand
Free-Video
ICTP Mathematics

Phase-Field Models for Motion by Mean Curvature - Lecture 4

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Explore advanced mathematical concepts in phase-field models and their application to motion by mean curvature, presented by a renowned expert from the University of Chicago.
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1 Lesons
1 hour 22 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
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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
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Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 22

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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 32 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 16

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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 27 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 10

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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 33 minutes
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Free-Video
Hausdorff Center for Mathematics

The Weighted Energy Dissipation WED Principle for Gradient Flows

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Explore advanced variational methods for gradient flows, focusing on the Weighted Energy Dissipation principle and its applications in metric spaces and optimal control problems.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
Isaac Newton Institute for Mathematical Sciences

Variational Methods in Image Processing and Advanced Materials Analysis - Kirk Lecture

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Explore variational methods in image processing and advanced materials analysis, focusing on density measures, image denoising, and quantum dot formation in semiconductors.
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1 Lesons
1 hour 13 minutes
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Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Existence of Solutions for the 2D Signorini-Coulomb Problem

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Explore solutions for 2D Signorini-Coulomb problem in static contact with Coulomb friction, comparing isotropic and anisotropic elasticity using Leray-Lions operator approach.
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1 Lesons
44 minutes
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Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Sobolev Homeomorphic Extensions in Geometric Analysis and Nonlinear Elasticity

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Explore Sobolev homeomorphic extensions in geometric analysis, focusing on boundary map properties and their implications for nonlinear elasticity and higher-dimensional problems.
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1 Lesons
37 minutes
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Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Fully Discrete Approximation Schemes for Rate-Independent Crack Propagation

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Explore convergence analysis of space-time discrete approximation schemes for rate-independent crack propagation in brittle elastic bodies, focusing on Griffith fracture criterion and local energy minimizers.
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1 Lesons
41 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Weak Limit of Homeomorphisms in W1,n-1: Invertibility and Lower Semicontinuity

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Explore weak limits of homeomorphisms, examining invertibility and lower semicontinuity in W1,n-1 spaces through variational and geometrical methods.
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14 Lesons
33 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Modern Trends in Gagliardo-Nirenberg Inequality

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Explore modern trends in Gagliardo-Nirenberg inequality, including generalizations, refinements, and applications in functional analysis and partial differential equations.
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1 Lesons
26 minutes
On-Demand
Free-Video
Conference GSI

A Variational Symplectic Scheme Based on Simpson's Quadrature

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Explore a variational symplectic scheme utilizing Simpson's quadrature, delving into its mathematical foundations and practical applications in numerical analysis.
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1 Lesons
17 minutes
On-Demand
Free-Video
Conference GSI

Conservation Laws as Part of Lagrangian Reduction - Application to Image Evolution

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Explore conservation laws in Lagrangian reduction and their application to image evolution, enhancing understanding of mathematical principles in visual processing.
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1 Lesons
22 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Maximization of Neumann Eigenvalues under Diameter Constraint

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Explore Neumann eigenvalue maximization under diameter constraints, delving into advanced spectral geometry concepts and mathematical analysis techniques.
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1 Lesons
49 minutes
On-Demand
Free-Video
BIMSA

Generic and Random Behavior of Minimal Surfaces

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Explore minimal surfaces in Differential Geometry, focusing on recent quantitative findings under genericity and randomness conditions. Discover spatial equidistribution and hyperbolic properties.
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1 Lesons
46 minutes
On-Demand
Free-Video
BIMSA

Optimal Estimates for Neumann Eigenvalues

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Explore optimal estimates for Neumann eigenvalues, including award-winning research on maximizing second eigenvalues and recent findings on convex set bounds.
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1 Lesons
50 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Mean Field Limit by Gamma Convergence

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Explores mean-field limit for λ-convex potentials using variational methods, focusing on gradient flows and Γ-convergence in interacting particle systems.
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1 Lesons
30 minutes
On-Demand
Free-Video
Kavli Institute for Theoretical Physics

Optimal and Variational Quantum Metrology and Vector Field Sensing - Peter Zoller

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Explore optimal quantum metrology and vector field sensing with Peter Zoller. Discover cutting-edge techniques in quantum sensing and their applications in fundamental physics research.
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1 Lesons
45 minutes
On-Demand
Free-Video
Institut Henri Poincaré

Some Open Mathematical Problems Concerning Charged Quantum Particles

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Explore open mathematical challenges related to charged quantum particles, delving into complex theoretical concepts and unsolved problems in quantum physics.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
Valence Labs

Removing Biases from Molecular Representations via Information Maximization

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Explore InfoCORE, an innovative approach to remove batch effects in drug screening data, enhancing molecular representations for improved property prediction and molecule-phenotype retrieval.
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4 Lesons
53 minutes
On-Demand
Free-Video
Simons Institute

On Gradient-Based Optimization - Accelerated, Distributed, Asynchronous and Stochastic

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Explore advanced gradient-based optimization techniques for machine learning, including accelerated, distributed, asynchronous, and stochastic methods, with insights from differential geometry and nonconvex optimization.
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16 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Variational Methods for Computational Microscopy - IPAM at UCLA

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Explore variational methods for computational microscopy with Stanley Osher, covering advanced techniques and applications in image processing and analysis.
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1 Lesons
40 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Regularity of Minimizers for a Model of Charged Droplets

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Explore the shape and properties of charged liquid droplets through a mathematical model, examining surface tension, repulsive forces, and the development of singularities in droplet formation.
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1 Lesons
59 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

From Phase Separation in Heterogeneous Media to Learning Training Schemes for Image Denoising

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Exploring variational approaches in phase separation and image denoising, focusing on heterogeneous media, geometric measure theory, and optimized training schemes for improved performance.
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1 Lesons
41 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Data Assimilation - Variational Methods - Lecture 8

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Explore variational methods in data assimilation for weather and climate modeling. Learn theoretical foundations and practical applications to enhance atmospheric state estimation and forecasting accuracy.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Minimization Problems for the Axisymmetric Neo-Hookean Energy

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Explore minimization problems for axisymmetric neo-Hookean energy, focusing on existence of minimizers, energy concentration, and bounds for relaxed energy in critical Sobolev cases.
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1 Lesons
38 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Non-interpenetration in Thin-film Models of Elastic Solids

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Explore non-interpenetration in thin-film models for elastic solids, focusing on dimension reduction, membrane regimes, and suitable conditions for preventing material penetration.
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1 Lesons
37 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Integral Representation and T-Convergence for Free-Discontinuity Problems

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Explore integral representation and T-convergence for free-discontinuity problems in GSBV p(.) space, focusing on variable exponent energies and their asymptotic behavior.
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1 Lesons
38 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Variational Methods for Hyperbolic Evolutions and Fluid-Structure Interactions

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Explore variational approaches to hyperbolic evolutions and fluid-structure interactions, focusing on well-posedness results for solid evolutions and fluid-solid interactions.
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1 Lesons
36 minutes
On-Demand
Free-Video
Yannic Kilcher

Set Distribution Networks - A Generative Model for Sets of Images

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Explores a novel framework for generating and encoding sets of images, introducing Set Distribution Networks that can create new object/identity sets while preserving key attributes.
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9 Lesons
59 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Path Constrained Unbalanced Optimal Transport

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Explore path constrained unbalanced optimal transport with Nicolas Charon, delving into geometric statistics and shape analysis applications.
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1 Lesons
43 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Injectivity in Second-Gradient Nonlinear Elasticity

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Explore injectivity in second-gradient nonlinear elasticity, delving into advanced mathematical concepts and their applications in materials science.
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1 Lesons
36 minutes
On-Demand
Free-Video
Probabilistic AI School

Variational Inference and Optimization - Lecture 3

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Explore advanced variational inference and optimization techniques for probabilistic AI, focusing on cutting-edge methods and practical applications.
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1 Lesons
45 minutes
On-Demand
Free-Video
AI Doctoral Academy

Variational Audio-Visual Representation Learning - Lecture 34

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Explore advanced concepts in variational learning techniques for audio-visual data representation, focusing on cutting-edge AI methodologies and their practical applications.
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1 Lesons
1 hour 15 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

New Dynamical Low-Complexity Approximations for the Schrödinger Equation

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Delve into advanced mathematical analysis of time-dependent Schrödinger equations, exploring new variational formulations and low-rank approximations for many-body electronic systems.
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1 Lesons
53 minutes
On-Demand
Free-Video