Harvard CMSA Courses

Machine Learning Tools for Mathematical Discovery

Explore ML tools like FunSearch and AlphaEvolve for mathematical discovery, comparing reinforcement learning and LLM-based approaches for finding interesting constructions.

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

Complete Calabi-Yau Metrics and Optimal Transport

Explore the connection between optimal transport and complete Calabi-Yau metrics on log varieties, bridging differential geometry and boundary regularity theory.

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

Automated Theory Formation and Interestingness in Mathematics

Explore how large language models synthesize interestingness measures to guide automated theory formation in elementary number theory from scratch.

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

About the Birch and Swinnerton-Dyer Conjecture

Explore the Birch and Swinnerton-Dyer Conjecture connecting elliptic curves' global invariants with local arithmetic properties through computational insights and mathematical development.

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

On the P-Curvature of Quantum Connections of Calabi-Yau Threefolds

Explore p-curvature of quantum connections in Calabi-Yau threefolds, connecting quantum Steenrod operations with BPS invariants and mirror symmetry in algebraic differential equations.

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

ReLU and Softplus Neural Networks as Zero-Sum Turn-Based Stopping Games

Discover how ReLU and Softplus neural networks can be interpreted as zero-sum turn-based stopping games, revealing their mathematical structure through game theory principles.

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

Symmetries of Periodic and Free Boundary Measures on Partitions

Explore the hidden distributional symmetry in periodic and free boundary q-Whittaker measures on partitions, including parameter exchanges and related Hall-Littlewood measures results.

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

Pfaffian Point Process for TASEP on the Half Line - Part 3

Delve into the Pfaffian point process for TASEP on the half line, exploring integrable systems with Jan De Gier from University of Melbourne.

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

Monitored Quantum Systems, Product of Random Matrices and Permutations

Explore the connections between monitored quantum systems, random matrix products, and permutations in this mathematical physics lecture by Andrea De Luca.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Ramanujan Property and Edge Universality of Random Regular Graphs

Explore the spectral properties of random d-regular graphs, focusing on eigenvalue rigidity and edge universality, and discover how these concepts relate to Ramanujan graphs and the Tracy-Widom distribution.

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

Multinomial Dimers and 3D Limit Shapes

Explore the multinomial dimer model on graphs, including partition function formulas and 3D limit shapes in the Aztec Diamond, based on Richard Kenyon's research with Catherine Wolfram.

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

Pfaffian Point Process for TASEP on the Half Line - Lecture 2 of 3

Explore the Pfaffian point process for TASEP on the half line in this advanced mathematical lecture by Jan De Gier, part of a series on integrable systems.

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

Random Partitions at High Temperature

Explore discrete particle ensembles and random partitions at high temperature, examining limiting measures and Markov chains through Jack symmetric polynomials and Fourier transforms.

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

Degeneration of Calabi-Yau 3-folds and 3-forms

Explore geometries of 3-forms on symplectic 6-manifolds and their applications to finding Lagrangian foliations in degenerate Calabi-Yau 3-folds through advanced differential geometry.

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

Sparsity and Symbols with Kolmogorov-Arnold Networks

Explore Kolmogorov-Arnold Networks theory, sparsity masks connecting deep nets to KANs, and symbolic regression applications with multimodal language models in this mathematical talk.

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