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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

L'œuvre d'Alexandre Grothendieck - The Mathematical Legacy of Alexandre Grothendieck

Découvrez les idées révolutionnaires d'Alexandre Grothendieck en mathématiques à travers l'analyse experte de Pierre Deligne, explorant notamment le formalisme des six foncteurs et ses contributions fondamentales.

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

Directed Metric Spaces, Alcoved Polytopes and Large Language Models

Explore the mathematical foundations of Large Language Models through directed metric spaces and alcoved polytopes, examining probability distributions, semantic structures, and categorical interpretations.

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

Cluster Structures on Kinematic Spaces - Particle Scattering and Flag Varieties

Delve into advanced particle physics concepts, exploring cluster structures in kinematic spaces through spinor helicity formalism and momentum twistor coordinates for modeling massless particle scattering.

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

Sum of Tensor Trace Invariants for Spin Glass Landscapes Optimization

Explore tensor trace invariants and random tensor theory techniques for optimizing spin glass landscapes, focusing on computational algorithms and theoretical frameworks for p-spin glass models.

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

Stable Adaptation and Learning in Nonlinear Systems and Neural Networks

Explore nonlinear systems tools for insights on collective computation and learning in large dynamical networks, focusing on stable adaptation and implicit sparse regularization.

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

Exploring Shallow Architectures for Image Classification

Explore shallow architectures for image classification, focusing on Scattering Networks and their potential compared to deep CNNs. Examine geometric arguments in deriving competitive representations.

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

Advanced Computational Imaging - Chassez le Naturel, Il Revient au Galop

Explorez les avancées en imagerie computationnelle, en mettant l'accent sur la stabilité et la fiabilité des réseaux neuronaux profonds pour la reconstruction d'images biomédicales.

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

Rapture of the Deep: Highs and Lows of Sparsity in Neural Networks

Explore sparsity in neural networks, its role in interpretability, and innovative optimization techniques beyond gradient descent for learning fast transforms.

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

Reliable AI: From Applied Harmonic Analysis to Quantum Computing

Explore reliable AI through generalization in graph neural networks and explainability using applied harmonic analysis. Delve into limitations of digital hardware and connections to quantum computing.

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