Institut des Hautes Etudes Scientifiques (IHES) Courses

Motives and Ring Stacks

Explore advanced cohomology theories through ring stacks, examining their connection to 6-functor formalism and motivic theory. Gain insights into Tannaka duality and analytic geometry applications.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Analytic Stacks: New Foundations for Analytic Geometry - Lecture 22/24

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.

• YouTube
• 1 hour 50 minutes
• Self-Paced
• Free Video

Analytic Stacks - Lecture 21

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with Peter Scholze.

• YouTube
• 1 hour 53 minutes
• Self-Paced
• Free Video

Analytic Stacks: New Foundations for Analytic Geometry

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.

• YouTube
• 2 hours 10 minutes
• Self-Paced
• Free Video

Analytic Stacks - Lecture 19

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with Peter Scholze.

• YouTube
• 1 hour 52 minutes
• Self-Paced
• Free Video

Analytic Stacks: New Foundations for Analytic Geometry - Lecture 18

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.

• YouTube
• 2 hours
• Self-Paced
• Free Video

Analytic Stacks: New Foundations for Analytic Geometry - Lecture 17

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.

• YouTube
• 1 hour 49 minutes
• Self-Paced
• Free Video

Mathematical General Relativity - Seventy-Two Years after Yvonne Choquet-Bruhat's Foundational Acta Paper

Explorez les avancées majeures en relativité générale mathématique depuis l'article fondateur d'Y.C. Bruhat, en examinant son impact durable sur le domaine.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

On the Canonical Geometric Structure of Initial Data for the Einstein Equations

Explore recent advancements in geometric foliations of asymptotically flat Riemannian manifolds and their connection to effective versions of the positive mass theorem. Delve into Schoen's conjecture and its implications.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

High Frequency Gravitational Waves and Einstein Equations with U(1) Symmetry

Explorez les travaux d'Yvonne Choquet-Bruhat sur les ondes gravitationnelles à haute fréquence et les solutions cosmologiques des équations d'Einstein avec symétrie U(1).

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Analytic Stacks - Lecture 16

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with Peter Scholze.

• YouTube
• 1 hour 53 minutes
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

Stability of Llarull's Theorem in All Dimensions

Explore stability of Llarull's theorem in all dimensions using spin geometry, with results in intrinsic flat and C^0-convergence outside small sets.

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

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video