Ricci Curvature Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

Spaces with Ricci Curvature Lower Bounds

Explore recent findings on spaces with nonnegative Ricci curvature, including singular set dimensions, fractal-like Weyl's laws, and nonproper Busemann functions in manifolds.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Synthetic Time-like Ricci Curvature Lower Bounds: The Isoperimetric Inequality

Explore synthetic timelike Ricci curvature lower bounds and their implications for isoperimetric inequality in Lorentzian synthetic spaces.

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

Institute for Pure & Applied Mathematics (IPAM)

Why Ricci Curvature (Almost) Failed Us in Noncommutative Dynamics

Explore the challenges of Ricci curvature in noncommutative dynamics and learn alternative approaches using Wasserstein distance-entropy inequalities, order inequalities, and Lipschitz norm in the Bakry-Emry program.

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

Hausdorff Center for Mathematics

Ricci Curvature and Fundamental Group in Riemannian Manifolds - Lecture 4

Explore fundamental groups in Riemannian manifolds with nonnegative Ricci curvature, examining structural properties, generation methods, and counterexamples to the Milnor conjecture.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Tamed Spaces: Dirichlet Spaces with Distribution-Valued Ricci Bounds

Explore Dirichlet spaces with distribution-valued Ricci bounds, focusing on tamed spaces theory and singular perturbations of Dirichlet form. Investigate integrated Bochner inequality and Bakry-Émery condition generalizations.

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

Harvard CMSA

RCD Structures on Singular Kähler Varieties

Explore RCD structures on 3D projective varieties with klt singularities, connecting algebraic geometry with Ricci curvature bounds and Nash entropy.

• YouTube
• 55 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

Institut des Hautes Etudes Scientifiques (IHES)

Nonnegative Ricci Curvature, Nilpotency, and Hausdorff Dimension

Explore nonnegative Ricci curvature, nilpotency, and Hausdorff dimension in relation to universal covers, minimal representing loops, and asymptotic cones of manifolds.

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

Institut des Hautes Etudes Scientifiques (IHES)

Ricci Curvature, Fundamental Group and the Milnor Conjecture - Part 2

Explore advanced concepts in topology and geometry, focusing on counterexamples to the Milnor conjecture and their construction using mapping class groups and asymptotic cones.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

A Sharp Isoperimetric-Type Inequality for Lorentzian Spaces Satisfying Time-Like Ricci Curvature Lower Bounds

Explore sharp isoperimetric-type inequalities in Lorentzian spaces with time-like Ricci curvature bounds, including applications to black holes and cosmological space-times.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Unified Synthetic Ricci Curvature Lower Bounds for Riemannian and Sub-Riemannian Geometries

Explore unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian geometries through gauge metric measure spaces. Discover recent advances in metric measure and sub-Riemannian spaces.

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

Institut des Hautes Etudes Scientifiques (IHES)

On Manifolds with Almost Non-Negative Ricci Curvature and Integrally-Positive Scalar Curvature

Explore advanced differential geometry through rigorous analysis of Riemannian manifolds with almost non-negative Ricci curvature and integral bounds on eigenvalues.

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

Institute for Pure & Applied Mathematics (IPAM)

On the Ricci Curvature Lower Bounds for Quantum Markov Semigroups

Delve into Ricci curvature lower bounds for quantum Markov semigroups, exploring intertwining techniques and functional inequalities in this mathematical physics presentation by Haonan Zhang.

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

Hausdorff Center for Mathematics

On the Equivalence of Distributional and Synthetic Ricci Curvature Lower Bounds

Explore the equivalence between distributional and synthetic approaches to defining lower Ricci curvature bounds on manifolds with continuous Riemannian metrics below C^2 regularity.

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