Scalar Curvature Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

Another Aspect of Gromov's Conjectures on Scalar Curvature

Explorez les conjectures de Gromov sur la courbure scalaire du point de vue de la relativité générale, en examinant leurs solutions partielles grâce au théorème de la masse positive.

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

Applied Algebraic Topology Network

Curvature Bounds and the Length of the Shortest Closed Geodesic

Explore upper bounds for shortest periodic geodesics on Riemannian manifolds, examining curvature's impact on closed geodesic length in various geometric contexts.

• YouTube
• 47 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

International Mathematical Union

Canonical Kaehler Metrics and Stability of Algebraic Varieties

Explore canonical Kähler metrics, algebraic variety stability, and the Yau-Tian-Donaldson conjecture in complex geometry. Delve into Kähler manifolds, curvature, and pluripotential theory with recent progress and applications.

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

ICTP Mathematics

Static Black Hole Uniqueness Theorems - Lecture 3

Explore asymptotic flatness, positive mass theorem, and scalar curvature in static black hole uniqueness theorems with expert Carla Cederbaum.

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

ICTP Mathematics

Some Geometric Properties of Spacetime - Lecture 2

Explore geometric properties of spacetime, including theorems on topology, dihedral angles, and scalar curvature, with insights on the positive mass theorem and Gauss-Bonnet theorem.

• YouTube
• 1 hour 18 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

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

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

Fields Institute

The Ground on Which We Stand

Explore the foundations of mathematical relativity, scalar curvature, and synthetic Lorentzian geometry in this thought-provoking lecture by Fay Dowker from Imperial College London.

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

IMSA

Almost Schur Lemma and Positivity Conditions in Quaternionic Contact Geometry

Explore quaternionic contact geometry, focusing on the Almost Schur Lemma and its implications for estimating qc scalar curvature under specific conditions.

• YouTube
• 45 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 dimension descent approach and recent extensions for scalar curvature problems.

• 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 this advanced mathematics lecture.

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

Institut des Hautes Etudes Scientifiques (IHES)

Index Theory and Applications to Scalar Curvature

Exploración de teoremas de índice para variedades compactas con borde y sus aplicaciones a la geometría de curvatura escalar, basado en trabajo conjunto con Brendle, Hanke y Wang.

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

Institut des Hautes Etudes Scientifiques (IHES)

Gromov's Rigidity Theorem for Polytopes with Acute Angles

Exploración de la conjetura de Gromov sobre la curvatura escalar de politopos convexos, incluyendo avances recientes y una nueva construcción de suavizado para el argumento de Gromov en casos de ángulos diedros agudos.

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