Institut des Hautes Etudes Scientifiques (IHES) Courses

Synthetic Data - Friend or Foe in the Age of Scaling?

Explore synthetic data's impact on AI scaling laws, model performance, and potential degeneration. Analyze theoretical frameworks and experimental findings for future AI development challenges.

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

Mathematics as a Translation Task - The Importance of Training Distributions

Explore how mathematical problems can be framed as translation tasks, focusing on the impact of training distributions on model performance and transformer model mechanics.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Grounding Large Language Models in Execution - From Code Generation to Formal Systems

Explore new training paradigms for grounding large language models in execution feedback, focusing on code generation and Lean proofstep prediction to bridge informal and formal LLM usages.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Three Problems in the Mathematics of Deep Learning

Explore mathematical concepts behind aligning neural networks with classical programs, including polynomial functors, cohomology, and higher categories.

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

Mathematical Structure Computed by Large Language Models - A First Approximation

Explore the mathematical structure of Large Language Models through directed metric spaces, polyhedra, and categorical interpretations. Gain insights into text extensions and restrictions.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

How Machine Learning Can Help Mathematicians

Explore AI's potential in mathematics: from language models guiding problem-solving to automated theorem proving, with real-world examples and future perspectives.

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

Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Perspectives - Lecture 4

Explore alternative viewpoints on quantum mechanics, including algebraic and geometric approaches. Examine concepts like decoherence, particles, scattering, and L-functionals to gain deeper insights into quantum theory.

• YouTube
• 1 hour 27 minutes
• Self-Paced
• Free Video

Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Perspectives - Part 3

Explore alternative viewpoints on quantum mechanics, including algebraic and geometric approaches. Gain insights into particle concepts, scattering, and L-functionals for solving infrared problems in quantum electrodynamics.

• YouTube
• 1 hour 47 minutes
• Self-Paced
• Free Video

Another Aspect of Gromov's Conjectures on Scalar Curvature

Explore Gromov's scalar curvature conjectures through general relativity, examining partial solutions via the positive mass theorem.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Geometric Variational Methods for Scalar Curvature and Other Curvature Problems

Explore geometric variational problems and their applications to curvature conditions, focusing on Schoen-Yau's approach and recent extensions.

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

Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Perspectives - Lecture 2

Explore alternative viewpoints to quantum mechanics, including algebraic and geometric approaches. Examine observables, states, and scattering concepts without relying on traditional textbook methods.

• YouTube
• 1 hour 42 minutes
• Self-Paced
• Free Video

Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Perspectives - Part 1

Explore alternative viewpoints on quantum mechanics, including algebraic and geometric approaches. Gain insights into particle concepts, scattering, and L-functionals for solving infrared problems in quantum electrodynamics.

• YouTube
• 1 hour 44 minutes
• Self-Paced
• Free Video

Integrality of the Betti Moduli Space

Explore the integrality of Betti moduli spaces for smooth projective varieties, examining representations of fundamental groups and their implications for algebraic geometry.

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

Weight Filtration on Log Crystalline Site

Explore advanced mathematical concepts in log crystalline site and weight filtration, focusing on p-adic Steenbrink complex construction for simple normal crossing log varieties.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Vanishing Theorems in Positive Characteristic

Explore vanishing theorems in positive characteristics, focusing on Kodaira and Kawamata-Viehweg theorems. Examine their applications, limitations, and recent developments in log Fano varieties and del Pezzo surfaces.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video