Harvard CMSA Courses

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

AI-Assisted Mathematics in Theorem Proving and Pattern Detection

Explore how AI revolutionizes mathematical discovery through theorem-proving, conjecture formulation, and pattern detection across various mathematical disciplines from geometry to number theory.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Exploring Patterns in Number Theory with Deep Learning - A Case Study with Möbius and Squarefree Indicator Functions

Explore how deep learning and neural networks can predict and analyze number theory patterns, focusing on the Möbius function and squarefree indicators in mathematical sequences.

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

Rigorous Results from Machine Learning Using Reinforcement Learning

Explore how Reinforcement Learning can prove mathematical theorems, focusing on applications in Number Theory and Knot Theory for solving complex mathematical problems and conjectures.

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

Image Generation by Score Diffusion and the Renormalisation Group

Delve into score-based diffusion models for image generation, exploring generalization capabilities, dimensionality challenges, and multiscale properties through statistical physics principles.

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

Solvable Models of Scaling and Emergence in Deep Learning

Delve into mathematical models explaining scaling behaviors and emergent properties in deep learning systems, with insights from Harvard's research on solvable frameworks and theoretical foundations.

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

Learning Euler Factors of Elliptic Curves with Transformers

Explore how machine learning and transformers can predict Euler factors of elliptic curves, uncovering patterns in L-functions and their relationship to the BSD conjecture.

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

Machine Learning L-functions - Analyzing Complex Functions in Number Theory

Explore machine learning applications in analyzing L-functions data, focusing on rational and non-rational functions to uncover patterns and predict mathematical invariants in number theory.

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

From Theorem Proving to Disproving: Modern Machine Learning versus Classical Heuristic Search

Explore how machine learning and classical methods compete in automated theorem proving and extremal graph theory, comparing their effectiveness in solving complex mathematical problems.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Sparse Subgraphs of the D-Cube with Diameter D

Explore mathematical optimization through PatternBoost algorithm to solve complex problems in hypercube diameter preservation and edge deletion in graph theory.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video