Harvard CMSA Courses

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

FunSearch: Mathematical Discoveries from Program Search with Large Language Models

Discover how FunSearch pairs large language models with systematic evaluation to make mathematical discoveries, surpassing existing results in combinatorics and algorithmic problem-solving.

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

Data Visualization with Category Theory and Geometry

Explore advanced mathematical foundations of data visualization through geometric and categorical perspectives, focusing on UMAP and dimensional reduction techniques for complex datasets.

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

Abelianization in Quantum Topology

Delve into advanced mathematical concepts exploring abelianization's role in quantum topology, including Chern-Simons invariants, skein algebras, and conformal blocks in this theoretical lecture.

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

Abelianization in Analysis of ODEs - Applications to Geometric Structures

Delve into advanced mathematical concepts of exact WKB method, exploring its connection to geometric theories and its role in analyzing ODEs through GL(N)-connections and Higgs bundles.

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

Heterotic Little String Theories and Inequivalent Genus-One Fibrations

Delve into supersymmetric quantum field theories, exploring T-duality in Little String Theories and their geometric connections to inequivalent genus-one fibrations in Calabi-Yau threefolds.

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

Mirror Construction for Nakajima Quiver Varieties

Explore the intricate relationship between quiver representation theory and mirror symmetry, focusing on Nakajima quiver varieties and their connection to Lagrangian immersions and ADHM construction.

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