Optimal Transport Courses and Certifications

Hausdorff Center for Mathematics

Mass Decompositions of Currents

Explore the mathematical theory of expressing normal currents as averages of integral currents, with insights into mass-decomposed currents and connections to optimal transportation problems.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Towards a Brenier Theorem on (P2(...(P2(H)…),W2) and Adapted Transport

Explore advanced mathematical concepts in optimal transport theory, focusing on Brenier's theorem extensions and adapted transport on probability measure spaces.

• YouTube
• 36 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Towards Stability of Trajectory Inference

Explore stability analysis of optimal transport methods for trajectory inference in biological development and gene expression data interpolation.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Properties of Diffusion Transport Maps via Creation of Log-Semiconcavity

Explore diffusion transport maps and their log-semiconcavity properties for asymptotically log-concave measures, establishing Lipschitz bounds and stability implications in generative modeling.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Regularity of the Quadratic Wasserstein Projections in the Convex Order

Explore regularity properties of quadratic Wasserstein projections in convex order, including continuity, non-expansiveness, and Hölder continuity for probability measures.

• YouTube
• 34 minutes
• Self-Paced
• Free Video

GERAD Research Center

A Transport Theoretic Perspective for Nonlinear Control

Explore transport theory's revolutionary approach to nonlinear control, bridging classical control problems with modern machine learning through measure-theoretic formulations and computational methods.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

INI Seminar Room 2

Tree-Based Diffusion Schrödinger Bridge with Applications to Wasserstein Barycenters

Delve into advanced mathematical concepts of Tree-Based Diffusion Schrödinger Bridge and its applications in Multi-marginal Optimal Transport, focusing on high-dimensional settings and Wasserstein barycenters.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

Trajectory Inference in Wasserstein Space

Explore advanced trajectory inference methods using Wasserstein geometry and B-spline approximation for analyzing dynamic processes in computational biology and point cloud data.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Valence Labs

Transport, Variational Inference and Diffusions

Explore connections between optimal transport and variational inference, focusing on stochastic differential equations and Girsanov transformations. Discover novel sampling and generative modeling techniques.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Valence Labs

A Computational Framework for Solving Wasserstein Lagrangian Flows

Explore a computational framework for solving Wasserstein Lagrangian flows, covering optimal transport variations and applications in single-cell trajectory inference.

• YouTube
• 1 hour 32 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Particle Methods for Optimization Over Measures - Lecture 3

Explore particle methods for measure optimization in this advanced lecture, covering theoretical foundations and practical applications in data science and machine learning.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

The Brownian Transport Map - IPAM at UCLA

Explore Lipschitz transport maps between probability measures, focusing on the Brownian transport map's construction, properties, and applications to Euclidean functional inequalities.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Blaschke-Santalo Inequality for Many Functions and Geodesic Barycenters of Measures

Explore geodesic barycenters and generalized Blaschke-Santalo inequality, deriving entropy bounds for Kantorovich cost in optimal transportation theory.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Particle Methods for Optimization Over Measures - Lecture 2

Explore particle methods for measure optimization, focusing on theoretical foundations and practical applications in data science and machine learning.

• YouTube
• 2 hours 19 minutes
• Self-Paced
• Free Video

Paul G. Allen School

Statistical Applications of Wasserstein Gradient Flows

Explore statistical applications of Wasserstein gradient flows in optimal transport, covering Otto calculus, Riemannian structures, and applications to variational inference and Gaussian mixture models.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video