Harvard CMSA Courses

The Einstein-Vlasov System in a Large Data Regime

Delve into advanced mathematical analysis of Einstein-Vlasov systems, exploring large data regimes, stability of Minkowski spacetime, and novel estimation techniques for Vlasov matter in relativistic contexts.

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

Quantum Cellular Automata - Understanding Evolution in Lattice Systems

Explore quantum cellular automata systems, focusing on lattice translations, topological phases, and locally generated subalgebras in discrete time evolution models.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Ranks of Elliptic Curves - A Survey of Rational Points and Group Structure

Explore the fundamental concepts of elliptic curves, their rational points, and group structures through an advanced mathematical examination of Mordell's theorem and contemporary research.

• YouTube
• 1 hour 24 minutes
• Self-Paced
• Free Video

Frontier of Formal Theorem Proving with Large Language Models - DeepSeek-Prover Series

Explore the latest developments in automated theorem proving using LLMs, focusing on DeepSeek-Prover's innovative approaches to mathematical reasoning and formal verification systems.

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

From Word Prediction to Complex Skills: Data Flywheels for Mathematical Reasoning

Explore how large language models develop mathematical reasoning abilities, from basic prediction to advanced problem-solving, through scaling laws, skill verbalization, and human-AI collaboration.

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

How Far Can Transformers Reason? The Globality Barrier and Inductive Scratchpad

Delve into transformer models' reasoning capabilities, exploring globality barriers, syllogistic composition, and how inductive scratchpads can enhance learning and generalization in AI systems.

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

Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning

Delve into imitation learning's theoretical foundations, exploring behavior cloning effectiveness, horizon dependencies, and sample complexity through a learning-theoretic lens with Dylan Foster.

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

Singularities in Fluids

Explore the complex dynamics of fluid singularities and their mathematical implications through advanced analysis of fluid behavior and mathematical modeling techniques.

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

AI for Mathematics - From Digitization to Intelligentization

Explore the evolving relationship between AI and mathematics, from historical interactions to cutting-edge research at Peking University, focusing on dataset formalization and future intelligent applications.

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

Learning the Topological Invariance of Knots

Dive into machine learning applications in knot theory, exploring neural networks for classifying topologically distinct knots and investigating the Jones unknot conjecture through innovative computational approaches.

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

Discovering New Mathematical Structures with Machine Learning

Explore how machine learning reveals hidden patterns in number theory and representation theory through collective analysis of mathematical structures and datasets.

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

Machine Learning Smooth 4-Genus of a Knot

Explore cutting-edge applications of machine learning in knot theory, focusing on computational methods for determining smooth 4-genus properties and their topological implications.

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

Generative Modeling with Flows and Diffusions - Applications to Scientific Computing

Explore generative modeling through flows and diffusions, focusing on mathematical foundations and applications in scientific computing, Monte Carlo sampling, and dynamical systems.

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

Learning the Effective Dynamics of Complex Systems

Explore advanced mathematical approaches for understanding and predicting complex system behaviors through machine learning and dynamic modeling techniques.

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

Machine Learning and Theorem Proving in Formal Languages

Explore how machine learning and neural networks can assist mathematicians in theorem proving, focusing on formal languages like Lean and addressing challenges in automated mathematical reasoning.

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