Harvard CMSA Courses

Homological Mirror Symmetry and Hodge Theory - January 2018

Explore advanced mathematical concepts in homological mirror symmetry, Hodge theory, and algebraic geometry through expert lectures from leading researchers in the field.

• YouTube
• 20 hours 7 minutes
• Self-Paced
• Free Video

Algebraic Methods in Combinatorics

Explore algebraic techniques solving major combinatorial problems like Kakeya, distinct distances, and cap-sets through expert talks from Harvard's 2017 workshop.

• YouTube
• 14 hours 32 minutes
• Self-Paced
• Free Video

Donaldson-Thomas and Gromov-Witten Theories

Explore advanced mathematical theories connecting Donaldson-Thomas and Gromov-Witten invariants through K3 fibrations, stable pairs, and S-duality conjectures in algebraic geometry.

• YouTube
• 12 hours 37 minutes
• Self-Paced
• Free Video

Topics in the Relation of Four-Manifold Invariants and Supersymmetric Field Theory

Explore advanced connections between four-manifold topology and supersymmetric quantum field theory, covering Donaldson invariants, Seiberg-Witten theory, and higher-dimensional extensions.

• YouTube
• 1 hour 13 minutes
• 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

Gromov-Hausdorff Limits of Collapsing Calabi-Yau Fibrations

Explore Gromov-Hausdorff limits of collapsing Calabi-Yau fibrations and their metric behavior, featuring recent progress on identifying limits with fibration bases using RCD properties.

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

Index from a Point - 4D N=2 SCFTs and Algebro-Geometric Characterization

Explore how protected data of 4d N=2 SCFTs can be characterized through algebro-geometric methods, focusing on Macdonald index reconstruction in Argyres-Douglas theories.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

On E7+1/2 Gauge Theory

Explore exotic E7+1/2 gauge theory in 6d F-theory through anomaly cancellation, M-theory geometry, and elliptic genus analysis of single-string worldsheet CFT.

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

Mathematics and Machine Learning Program - September 3 to November 1, 2024

Explore cutting-edge intersections of mathematics and AI through expert talks on theorem proving, neural networks, and automated mathematical discovery at Harvard CMSA.

• YouTube
• 2 days 18 hours 48 minutes
• Self-Paced
• Free Video

Yang-Mills and the Foundations of Quantum Field Theory

Explore the mathematical foundations of Yang-Mills theories and quantum field theory, covering the Clay Millennium Prize problem and recent progress in constructive field theory.

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

RCD Structures on Singular Kähler Varieties

Explore RCD structures on 3D projective varieties with klt singularities, connecting algebraic geometry with Ricci curvature bounds and Nash entropy.

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

Discretization and Distribution Learning in Diffusion Models

Explore discretization techniques and distribution learning in diffusion models, covering randomized midpoints, score matching, and applications to parameter estimation and density learning.

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

The Value of Side Information in Unlabeled Data

Discover how side information in unlabeled data improves machine learning models through iterative pseudo-labeling and error decorrelation analysis.

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

Negative Stepsizes Make Gradient-Descent-Ascent Converge

Discover how negative stepsizes enable Gradient-Descent-Ascent convergence on min-max problems through innovative time-varying, asymmetric stepsize schedules and slingshot dynamics.

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

Self-play LLM Theorem Provers with Iterative Conjecturing and Proving

Explore self-play reinforcement learning for theorem proving where LLMs act as both conjecturers and provers, achieving state-of-the-art results on mathematical benchmarks.

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