Institut des Hautes Etudes Scientifiques (IHES) Courses

Spacetime Harmonic Functions and Applications in Positive Mass Theorems and Comparison Geometry

Explore recent developments in level set techniques for elliptic equations, focusing on spacetime harmonic functions and their applications to positive mass theorems and comparison geometry.

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

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

Gromov's Rigidity Theorem for Polytopes with Acute Angles

Explore recent developments in dihedral rigidity, focusing on Gromov's conjecture and Brendle-Wang's alternative smoothing construction for polytopes with acute angles.

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

Birational Invariants from Gromov-Witten Theory - Lecture 2

Explore birational invariants derived from Gromov-Witten theory, focusing on Iritani's theorem and its applications to proving non-rationality of algebraic varieties.

• YouTube
• 2 hours 14 minutes
• On-Demand
• Free Video

Analytic Stacks - Lecture 6

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 49 minutes
• On-Demand
• Free Video

Analytic Stacks - Lecture 5

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 46 minutes
• On-Demand
• Free Video

Birational Invariants from Gromov-Witten Theory - Lecture 1

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 6 minutes
• On-Demand
• Free Video

Analytic Stacks - Lecture 3

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

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

Analytic Stacks - Lecture 2

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 43 minutes
• On-Demand
• Free Video

Analytic Stacks - Lecture 1/24

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

• YouTube
• 1 hour 50 minutes
• On-Demand
• Free Video

Mock Plectic Points in Hilbert Modular Surfaces and Elliptic Curves

Explore the analogy between Hilbert modular surfaces and mock counterparts, examining plectic philosophy in mock Hilbert settings and its implications for elliptic curves of rank two over Q.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Period Relations for Arithmetic Automorphic Periods on Unitary Groups

Explore period relations for arithmetic automorphic periods on unitary groups, focusing on Petersson inner products and connections to L-function special values.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Shimurian Generalizations of Truncated Barsotti-Tate Groups - After V. Drinfeld

Explore Drinfeld's Shimurian analogs of truncated Barsotti-Tate groups, prismatic F-gauges, and their algebraicity in this advanced mathematical lecture.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

On the Cohomology of Shimura Varieties with Torsion Coefficients

Explore recent advances in Shimura varieties' cohomology with torsion coefficients, including Hodge-Tate period morphism geometry and local-global compatibility insights.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Hidden Symmetries of the Work of Jan Nekovář

Explorez les principes unificateurs de la recherche de Jan Nekovar, des systèmes d'Euler aux variétés de Shimura quaternioniques, en passant par les résultats de parité pour les fonctions L.

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