Harvard CMSA Courses

Peano: Learning Formal Mathematical Reasoning Without Human Data

Discover how AI systems can learn mathematical reasoning through autonomous exploration, focusing on theorem proving and algebra problem-solving without relying on human training data.

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

How to Train Deep Neural Networks to Think Strategically

Delve into the intersection of Deep Learning and Game Theory, exploring strategic neural network training, Nash equilibria challenges, and innovative approaches to DNN optimization in gaming and adversarial scenarios.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

What Mathematics Can Help Us Understand and Advance Machine Learning - ML, QML, and Dynamics

Explore the mathematical foundations of machine learning through dynamic systems, chaos theory, and tensor structures, examining their roles in neural networks and language models.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Algebraic Varieties in Quantum Chemistry

Explore the mathematical foundations of coupled cluster theory in quantum chemistry, focusing on algebraic geometry's role in solving electronic Schrödinger equations and truncation varieties.

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

Remarks on Physical Mathematics and Quantum Field Theory

Explore the dynamic interplay between mathematics and theoretical physics through Stokes' phenomenon, quantum field theory, and differential topology of four-manifolds in modern scientific research.

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

Modelling Hybrid Zones - Mathematical Models in Population Genetics

Explore mathematical models in population genetics, focusing on natural selection, spatial structure, and genetic drift to understand how domain shapes influence species' evolution.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

All-Loop Scattering as a Counting Problem

Delve into advanced theoretical physics as Nima Arkani-Hamed explores a revolutionary approach to understanding scattering amplitudes through combinatorial concepts and kinematic space analysis.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Fluid Stabilization in Slowly Expanding Cosmological Spacetime

Explore relativistic fluid dynamics in expanding spacetimes, examining shock formation suppression and its implications for cosmological structure formation and evolution.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Llemma: An Open Language Model for Mathematics

Discover how Llemma, a powerful language model, revolutionizes mathematical computing through advanced capabilities in theorem proving, tool usage, and mathematical reasoning using the Proof-Pile II dataset.

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

Resolving Memory in Numerical Relativity and Fixing BMS Frames for Modeling

Delve into numerical relativity's advanced techniques for modeling binary black hole mergers, focusing on memory effects, BMS frames, and precision waveform extraction methods.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Physics of Language Models: Knowledge Storage, Extraction, and Manipulation

Delve into the mechanics of how large language models store, extract, and manipulate knowledge, exploring key findings about memory capabilities and limitations in AI systems through empirical research.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Breaking Ergodicity - Quantum Scars and Regular Eigenstates

Delve into quantum many-body scars and their role in breaking ergodicity, exploring connections between quantum billiards, spinor condensates, and the Eigenstate Thermalization Hypothesis.

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

Chern Mosaic and Ideal Bands in Helical Trilayer Graphene

Delve into the physics of helical trilayer graphene, exploring Chern mosaic patterns, flat band properties, and their relationship to quantum phenomena in emergent real-space structures.

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

LeanDojo - Theorem Proving with Retrieval-Augmented Language Models

Explore how LeanDojo leverages retrieval-augmented language models to enhance automated theorem proving, featuring open-source tools and innovative premise selection techniques.

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

Tidal Squeezing of Black Holes

Explore the fascinating phenomenon of Kerr black holes' resistance to deformation and the dynamics of tidal squeezing through advanced gravitational field analysis and hidden symmetries.

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