Vector Fields Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 2

Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.

• YouTube
• 1 hour 48 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 1

Explore modern concepts in flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics and turbulence theory.

• YouTube
• 1 hour 46 minutes
• On-Demand
• Free Video

Discover AI

Beyond Mamba AI: Vector Fields and Fluid Dynamics in Transformer Models - Session 6

Explore the intersection of fluid dynamics and AI transformers, examining mathematical frameworks and theoretical physics concepts to enhance understanding of advanced neural network architectures.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Unsupervised Features Learning for Sampled Vector Fields

Explore innovative techniques for analyzing sampled vector fields using graph structures and unsupervised learning, revealing hidden features correlated with known dynamics in analytical models.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Fields Institute

New Techniques for the Resolution of Singularities of Vector Fields and Differential Operators

Explore advanced techniques for resolving singularities in vector fields and differential operators, covering localization, geometric theorems, and coordinate systems for complex mathematical analysis.

• YouTube
• 1 hour 44 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

The Classification of Finite-Dimensional Lie Algebras of Hamiltonian Vector Fields on the Plane

Explore finite-dimensional Lie algebras of Hamiltonian vector fields on the plane, their classification, properties, and applications in studying Hamiltonian systems.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Barcodes for the Topological Analysis of Gradient-Like Vector Fields

Explore topological analysis of gradient-like vector fields using barcodes. Learn about chain complexes, parametrization, and applications in smooth and discrete settings, with insights on stability and approximation.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

IMSA

Chern Classes and Indices of Vector Fields on Singular Varieties

Explore Chern classes and vector field indices on singular varieties, examining fundamental invariants in geometry and topology and their evolving theory for non-smooth spaces.

• YouTube
• 53 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 5

Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.

• YouTube
• 1 hour 55 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 3

Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.

• YouTube
• 1 hour 47 minutes
• On-Demand
• Free Video

Fields Institute

Integrating Vector Fields on Subcartesian Spaces

Explore advanced mathematical concepts in vector field integration on subcartesian spaces with expert Yael Karshon, part of a broader workshop and program on toric topology.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Global Noncommutative Geometry Seminar

The Helffer-Nourrigat Conjecture - Hypoellipticity and Fredholmness of Polynomials of Vector Fields

Explore hypoellipticity and Fredholmness in vector field polynomials through the Helffer-Nourrigat Conjecture, advancing understanding in noncommutative geometry.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Valence Labs

Meta Flow Matching - Integrating Vector Fields on the Wasserstein Manifold

Explore advanced flow-based modeling techniques for predicting biological system dynamics, focusing on population-level evolution and personalized medicine applications using Graph Neural Networks.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Decorrelation of Vector Fields with Speed of Varifolds

Explore the mathematical concept of decorrelation between diffeomorphic deformations using varifold speeds, focusing on shape registration and model interpretability in infinite-dimensional geometry.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Vector Fields on the Hyperbolic Plane and Surfaces in Half-Pipe Space

Explore the relationship between vector fields on hyperbolic planes and surfaces in half-pipe space, examining Mess's ideas and their applications in Teichmüller theory and geometric extensions.

• YouTube
• 47 minutes
• On-Demand
• Free Video