Scalar Curvature Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

Another Aspect of Gromov's Conjectures on Scalar Curvature

Explore Gromov's scalar curvature conjectures through general relativity, examining partial solutions via the positive mass theorem.

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

Global Noncommutative Geometry Seminar

Index Pairing and Quantitative Control of Scalar Curvature

Explore index pairing and quantitative scalar curvature control in noncommutative geometry, focusing on direct operators, enlargibility, and metric space theory.

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

Institut des Hautes Etudes Scientifiques (IHES)

Scalar Curvature via Dirac Eigenvalues

Explore advanced differential geometry connecting scalar curvature to Dirac eigenvalues, covering Llarull's theorem, Geroch conjecture, and Yamabe invariant relationships.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Conference GSI

Monotonicity of the Scalar Curvature of the Quantum Exponential Family for Transverse-Field Ising

Explore scalar curvature monotonicity in quantum exponential family for transverse-field Ising chains, examining finite-size effects and implications for Petz conjecture.

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

Hausdorff Center for Mathematics

Lipschitz Rigidity for Scalar Curvature

Explore the extremality and rigidity phenomena of lower scalar curvature bounds on spin Riemannian manifolds, focusing on Lipschitz rigidity generalizations and connections between spin geometry and quasiconformal mappings.

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

Institute for Advanced Study

Notions of Scalar Curvature - Mikhail Gromov

Explore scalar curvature concepts, spin bundles, and rich curves with renowned mathematician Mikhail Gromov in this advanced topology lecture from the Institute for Advanced Study.

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

Applied Algebraic Topology Network

Yevgeny Liokumovich - Urysohn Width, Isoperimetric Inequalities and Scalar Curvature

Explore metric spaces, Hausdorff measure, and continuous mappings. Discover connections to isoperimetric inequalities and Riemannian geometry's positive scalar curvature.

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

Centre de recherches mathématiques - CRM

Scalar Curvature Rigidity of Polytopes

Explore Riemannian metrics and scalar curvature positivity in differential geometry. Delve into Gromov's comparison principle for polytopes and recent advancements in verifying his conjecture.

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

Institut des Hautes Etudes Scientifiques (IHES)

Width, Scalar Curvature and Macroscopic Scalar Curvature

Explore the interplay between positive scalar curvature and macroscopic scalar curvature, examining Urysohn width and closed geodesics in PSC and PMSC spaces.

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

Institut des Hautes Etudes Scientifiques (IHES)

Geometric Variational Methods for Scalar Curvature and Other Curvature Problems

Explore geometric variational problems and their applications to curvature conditions, focusing on Schoen-Yau's approach and recent extensions.

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

Institut des Hautes Etudes Scientifiques (IHES)

Positive Mass Theorem and Positive Scalar Curvature with Singularities

Explore recent developments in positive mass theorem and scalar curvature, focusing on singular metrics and isolated conical singularities in mathematical physics.

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

Institut des Hautes Etudes Scientifiques (IHES)

Global Effects of Positive Scalar Curvature in Geometry

Explorez les effets globaux de la courbure scalaire positive, y compris le problème de remplissage de Gromov et les théorèmes de type Llarull sur les variétés complètes.

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

Institut des Hautes Etudes Scientifiques (IHES)

Index Theory and Applications to Scalar Curvature

Explore index theorems for compact manifolds with boundary and their applications to scalar curvature geometry, focusing on Dirac operators and boundary value problems.

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

Institut des Hautes Etudes Scientifiques (IHES)

Smoothing by Ricci-DeTurck Flow and Applications to Scalar Curvature

Explore Ricci-DeTurck flow's existence theory for non-smooth initial metrics and its applications to scalar curvature rigidity problems in geometry.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Scalar Curvature Rigidity in Manifolds

Explore scalar curvature rigidity in manifolds, examining known solutions and current research questions using spinorial techniques.

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