Curvature Courses and Certifications

Insights into Mathematics

The Curvature of a Parabola, Without Calculus - Rational Geometry Math Foundations

Algebraic approach to calculate parabola curvature without calculus, using circle circumquadrance and triangle properties. Demonstrates wider applicability to various algebraic curves.

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

Institut des Hautes Etudes Scientifiques (IHES)

Geometry in Non-Positive Curvature and Kähler Groups

Explore advanced geometric group theory through expert lectures on hyperbolic geometry, Kähler groups, and their interactions in this specialized mathematical conference.

• YouTube
• 10 hours 11 minutes
• On-Demand
• Free Video

Centrum Fizyki Teoretycznej PAN

SCREAM Seminar - Symmetry, Curvature Reduction, and Equivalence Methods in Differential Geometry

Explore advanced differential geometry through Cartan and parabolic geometries, covering conformal structures, integrable systems, and applications to cosmology and quantum theory.

• YouTube
• 2 days 16 hours 39 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Probabilistic Methods in Negative Curvature - 2023

Explore advanced probabilistic techniques in negative curvature geometry through expert lectures on diffeomorphism groups, hyperbolic rigidity, and random walks on groups.

• YouTube
• 1 day 8 hours 13 minutes
• On-Demand
• Free Video

Using Curvature to Understand the Structure of Dynamics

Explore curvature's role in understanding attractor dynamics and its application in time-series data reconstruction, focusing on optimal time-delay parameter selection for delay-coordinate embeddings.

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

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
• On-Demand
• Free Video

Applied Algebraic Topology Network

Curvature Variation Based Sampling for Delaunay Triangulations of Manifolds

Explore adaptive sampling for Delaunay triangulations of Riemannian manifolds, focusing on curvature variation and quality bounds for successful triangulation. Learn about geometric realizations and manifold triangulation techniques.

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