Curvature Courses and Certifications

International Centre for Theoretical Sciences

Zero Mean Curvature Surfaces in Euclidean and Lorentz-Minkowski 3-Space - Lecture 1

Explore zero mean curvature surfaces in Euclidean and Lorentz-Minkowski spaces, covering fundamental concepts, variations, stability, and examples of minimal surfaces with diverse properties and geometries.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

How Optimal Transport Can Help Us to Determine Curvature of Complex Networks

Explore Ollivier Ricci curvature in complex networks, its applications in network analysis, and implementation in chemical reaction networks using optimal transport theory.

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

IMSA

Curvature Formula for Direct Images of Relative Canonical Bundles with Poincaré Type Twist

Curvature formula for direct images of relative canonical bundles with Poincaré type twist, improving positivity results and potentially proving Kobayashi hyperbolicity of moduli spaces.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

IMSA

Holomorphic Bisectional Curvature and Applications to Deformations and Rigidity of Mixed Hodge Structure

Explore holomorphic bisectional curvature in Hodge theory, focusing on mixed Hodge metrics, rigidity results, and applications to geometric examples.

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

Hausdorff Center for Mathematics

Ricci Curvature and Functional Inequalities for Interacting Particle Systems

Explore entropic Ricci curvature bounds and their applications to interacting particle systems, focusing on functional inequalities and convergence rates to equilibrium in nonnegative curvature scenarios.

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

Hausdorff Center for Mathematics

Curvature of the Determinant Line Bundle for Noncommutative Tori

Explore differential geometry of curved noncommutative tori, including spectral invariants and curvature of determinant line bundle for Dirac operators on noncommutative two tori.

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

ICTP Mathematics

Motion by Curvature of Networks in the Plane - Lecture 4

Explore motion by curvature of planar networks, covering collapse, parametrization, evolution equations, special cases, singularities, and localization. Gain insights into this advanced mathematical topic.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Phase-Field Models for Motion by Mean Curvature - Lecture 2

Explore phase-field models for motion by mean curvature, covering topics like skew symmetry, levelsets, distance functions, and classical statements with expert Panagiotis Souganidis.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Singularities of the Mean Curvature Flow of Mean Convex Hypersurfaces - Lecture 5

Explore singularities in mean curvature flow of convex hypersurfaces, covering max inequality, weak solutions, surgeries, and Type 2 singularities with intuitive explanations.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Society for Industrial and Applied Mathematics

Mean Curvature Flow, Neural Networks, and Applications

Explore mean curvature flow's applications in image processing, data science, and biology. Learn how neural networks can approximate interface evolutions for non-oriented surfaces, with applications to Steiner and Plateau problems.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Conference Talk

Fields Institute

Quantitative Operator K-Theory, Positive Scalar Curvature and Filling Radius

Explore connections between quantitative operator K-theory, positive scalar curvature, and filling radius in this advanced mathematics talk by Guoliang Yu.

• YouTube
• 54 minutes
• Self-Paced
• Conference Talk

Fields Institute

Low-Dimensional Approximations of the Conditional Law of Volterra Processes - A Non-Positive Curvature Approach

Explore non-positive curvature approaches for approximating conditional laws of Volterra processes in low dimensions, with applications in machine learning and dynamical systems.

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

International Centre for Theoretical Sciences

Zero Mean Curvature Surfaces in Lorentz Minkowski Spaces - Lecture 3

Explore zero mean curvature surfaces in Lorentz-Minkowski spaces with expert Shoichi Fujimori. Delve into advanced geometric concepts and their applications in this specialized lecture.

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

International Centre for Theoretical Sciences

Zero Mean Curvature Surfaces in Lorentz Minkowski Spaces - Lecture 2

Explore zero mean curvature surfaces in Lorentz-Minkowski spaces with expert Shoichi Fujimori. Delve into advanced geometric concepts and their applications in this specialized lecture.

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

International Centre for Theoretical Sciences

Zero Mean Curvature Surfaces in Lorentz Minkowski Spaces - Lecture 1

Explore zero mean curvature surfaces in Lorentz-Minkowski spaces with expert Shoichi Fujimori. Gain insights into this evolving field of mathematical research and its applications.

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