Curvature Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

The Non-Abelian p-Curvature Conjecture

Explore a generalized p-curvature conjecture for non-linear ODEs, its implications for algebraic geometry, and proof techniques inspired by Katz and Esnault-Groechenig's work.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Fields Institute

Quantum Ricci Curvature and Quantum Gravity

Explore quantum Ricci curvature's role in quantum gravity theories, examining its implications for spacetime structure and gravitational interactions at the quantum level.

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

Fields Institute

Introduction to the Riemannian Curvature Dimension Condition - Lecture 3

Explore advanced concepts in Riemannian geometry with Prof. Gigli, focusing on the Curvature Dimension condition and its applications in non-smooth settings.

• YouTube
• 1 hour 42 minutes
• Self-Paced
• Free Video

Fields Institute

Introduction to the Riemannian Curvature Dimension Condition - Lecture 2

Explore advanced concepts in Riemannian geometry with Prof. Gigli, focusing on the Curvature Dimension condition and its applications in non-smooth settings.

• YouTube
• 1 hour 38 minutes
• Self-Paced
• Free Video

Fields Institute

Introduction to the Riemannian Curvature Dimension Condition - Lecture 1

Explore the Riemannian Curvature Dimension condition with Professor Nicola Gigli, delving into advanced mathematical concepts for graduate-level understanding of non-smooth geometry.

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

Fields Institute

Timelike Curvature-Dimension Conditions for Lorentzian Spaces via Rényi's Entropy

Explore timelike curvature-dimension conditions in Lorentzian spaces using Rényi's entropy, advancing understanding of low regularity physics and geometry in spacetime.

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

ICTP Mathematics

Math Associates Seminar- Bubbling of Q-Curvature Equation on 4-Manifolds in the Null Case

Explore the Q-curvature equation on 4-manifolds, focusing on solution behavior as ε approaches zero. Gain insights into the Paneitz operator and sign-changing functions in mathematical analysis.

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

ICTP Mathematics

Fractional Poincare Inequalities on Manifolds With Finite Total Q-Curvature

Explore fractional Poincare inequalities on manifolds, focusing on finite total Q-curvature. Advanced mathematical concepts for geometry and physics enthusiasts.

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

ICTP Mathematics

Curves and Surfaces with Constant Nonlocal Mean Curvature

Explore constant nonlocal mean curvature in curves and surfaces, examining advanced mathematical concepts and their applications in geometry and physics.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Dynamics and Symmetry of Ancient Convex Mean Curvature Flows - Lecture 5

Explore dynamics and symmetry of ancient convex mean curvature flows in this advanced mathematics lecture by Sigurd Angenent from the University of Wisconsin-Madison.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Dynamics, Symmetry and Asymmetry of Ancient Solutions to Mean Curvature Flow - Ancient Convex Solutions to MCF

Explore ancient convex solutions to Mean Curvature Flow, examining dynamics, symmetry, and asymmetry in this advanced mathematics lecture by Sigurd Angenent.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video