Institut des Hautes Etudes Scientifiques (IHES) Courses

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Analytic Stacks: New Foundations for Analytic Geometry - Lecture 15

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

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

Analytic Stacks - Lecture 14

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

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

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

Analytic Stacks - Lecture 12

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

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

Analytic Stacks - New Foundations for Analytic Geometry - Lecture 11/24

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

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

Birational Invariants from Gromov-Witten Theory - Lecture 4

Explore birational invariants derived from Gromov-Witten theory, focusing on Iritani's theorem and its applications to proving non-rationality of geometric objects like cubic 4-folds.

• YouTube
• 2 hours 23 minutes
• On-Demand
• Free Video

Solving Equations from Combinatorics via Computer Algebra

Explore advanced techniques for solving discrete differential equations in combinatorics using computer algebra, focusing on efficient methods for n=2 cases and recent developments in systems of equations.

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

Combinatorial Topological Quantum Field Theories and Geometrical Applications

Explore combinatorial topological quantum field theories, focusing on partition functions, group representations, and integrality properties in character tables. Uncover connections between physics and mathematics.

• YouTube
• 55 minutes
• On-Demand
• 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 with renowned mathematician Peter Scholze.

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

Cartes Aléatoires - Entre Croissance et Fragmentation

Explorez les liens fascinants entre cartes aléatoires et processus de croissance-fragmentation dans cette conférence captivante sur les surfaces aléatoires et la dynamique des particules.

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

Géométrie des Cartes Aléatoires Décorées : L'Exemple du Modèle de Boucles O(n)

Explorez la géométrie des cartes aléatoires décorées à travers le modèle de boucles O(n). Découvrez le diagramme de phase, les exposants critiques et la solution exacte de ce modèle de physique statistique.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Dénombrement de Cartes : Entre Combinatoire, Probabilités et Mathématiques

Explorez le dénombrement des cartes mathématiques, ses approches variées et ses applications en combinatoire, probabilités et physique.

• YouTube
• 2 hours 1 minute
• On-Demand
• Free Video