Harvard CMSA Courses

The Poincaré Conjecture and Mathematical Discovery

Explore the Poincaré Conjecture through topology and differential equations, examining its proof by Hamilton and Perelman and broader impact on mathematical discovery.

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

Understanding Optimization in Deep Learning with Central Flows

Explore how central flows reveal the hidden dynamics of deep learning optimization, explaining why gradient descent succeeds even when loss increases and how adaptive optimizers navigate complex landscapes.

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

Non-Perturbative Aspects of Self-Dual Gauge Theory

Explore non-perturbative effects in self-dual gauge theory, including beta-function computations via Grothendieck-Riemann-Roch and holographic methods, plus novel QCD calculations.

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

Graph Integrals on Kähler Manifolds

Explore convergence of graph integrals on analytic Kähler manifolds and their applications to constructing geometric invariants of Calabi-Yau metrics in holomorphic quantum field theory.

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

Global Epistasis in Genotype-Phenotype Maps

Explore how genetic interactions shape trait expression through global epistasis patterns in genotype-phenotype mapping with Princeton researcher Gautam Reddy.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Thinking About High-Dimensional Biological Data in the Age of AI

Explore AI's promise and limitations in biology through transformer models for genotype-phenotype mapping and LLM-based cellular identity analysis, comparing complex AI with simpler methods.

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

Superintelligence for Scientific Discovery

Explore how multi-agent AI swarms transcend prediction to become invention partners, generating novel discoveries in protein design and music through structured creativity.

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

Applications of Euclidean Neural Networks to Understand and Design Atomistic Systems

Explore Euclidean neural networks for atomistic systems, covering 3D symmetries, molecular property prediction, and materials design with state-of-the-art AI approaches.

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

Data Reliability Scoring

Discover how to assess dataset reliability without ground truth using the Gram Determinant Score method for noisy, biased, or strategically manipulated data in data-driven decisions.

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

What Does Machine Learning Have to Offer Mathematics?

Explore how machine learning techniques can revolutionize mathematical research and problem-solving approaches in this Harvard CMSA conference presentation.

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

The Origin of the Indo-Europeans

Discover how DNA from ancient fossils reveals the origins and spread of Indo-European languages, the world's largest language family with over 3 billion speakers.

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

Accelerating the Discovery of van der Waals Quantum Materials Using AI

Discover how AI accelerates the exploration of van der Waals quantum materials, combining machine learning with density functional theory to predict magnetic and topological properties.

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

Orientifolds for F-theory on K3 Surfaces

Explore F-theory orientifolds on elliptically fibered K3 surfaces, connecting string theory compactification with D-brane classifications using real K-theory and antiholomorphic involutions.

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

Nonlinear Random Matrices in High-Dimensional Estimation and Learning

Explore equivalence principles connecting nonlinear random matrices to simpler models, with applications to kernel methods, random features, and Transformer networks.

• YouTube
• 17 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