Institut des Hautes Etudes Scientifiques (IHES) Courses

Thirty-Six Entangled Officers of Euler: Quantum Solution to a Classical Problem

Explore quantum combinatorial designs and their application in solving Euler's 36 officers problem, revealing insights into quantum information processing and error detection.

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

The Miracle of Integer Eigenvalues in Finite Poset Matrices

Explore the fascinating connection between finite posets and integer eigenvalues in matrix theory, with implications for symmetric group representations.

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

Periods of Hypersurfaces via Effective Homology

Explore numerical approximations of periods for hypersurfaces using effective homology, enabling computation of algebraic invariants for complex projective varieties.

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

Counting Partitions by Genus

Explore set partition counting by genus, focusing on primitive partitions and functional equations to reconstruct all partitions, with emphasis on genus 0-2 cases.

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

The Nullstellensatz and Positivstellensatz for Sparse Tropical Polynomial Systems

Explorez les avancées en algèbre tropicale, notamment le Nullstellensatz et le Positivstellensatz pour les systèmes polynomiaux tropicaux clairsemés, avec des applications aux jeux à paiement moyen paramétrique.

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

Counting Restricted Set Partitions with Hypergeometrics

Explore advanced set partition counting using hypergeometric functions and generalized Hermite polynomials. Gain insights into restricted Bell numbers and their closed-form expressions.

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

Fock Spaces Associated with Coxeter Groups of Type B

Explore Fock spaces related to infinite hyperoctahedral groups, examining two-parameter functions and their positive definiteness in extreme characters. Apply findings to cyclic Fock spaces of type B.

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

Perception of Visual Art and Topological Data Analysis

Explore topological data analysis applications in visual art perception, comparing eye movements for abstract paintings vs. AI-generated images using algebraic topology methods.

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

Pourquoi la grossesse et l'accouchement sont-ils encore si mortels ?

Explorez les causes de la mortalité maternelle mondiale et les solutions potentielles avec l'experte de l'OMS Marleen Temmerman.

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

Analytic Stacks: New Foundations for Analytic Geometry - Lecture 7/24

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

• YouTube
• 1 hour 36 minutes
• On-Demand
• Free Video

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