Harvard CMSA Courses

Chaos and Complexity in Quantum Dynamics

Explore quantum chaos and complexity through advanced mathematical frameworks connecting geometry with quantum dynamics in this Harvard physics seminar.

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

The Hodge Locus

Explore recent results on Hodge locus distribution in mixed variations of Hodge structures with concrete applications to moduli spaces.

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

Tame Geometry and Hodge Theory

Discover applications of o-minimality in complex geometry and Hodge theory through an expert introduction to tame geometric structures and their mathematical foundations.

• YouTube
• 1 hour 40 minutes
• Self-Paced
• Free Video

The P vs. NP Problem - An Existential Question for Mathematics

Explore the profound P vs NP problem and its implications for mathematics, computing, and automated proof search in this millennium prize lecture by Harvard's Madhu Sudan.

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

Ramanujan Property of Random Regular Graphs and Delocalization of Random Band Matrices

Explore edge universality in random regular graphs and delocalization in random band matrices, covering Ramanujan properties and eigenvalue statistics with Tracy-Widom distributions.

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

Extracting Bar Lengths from Multiparameter Persistent Homology

Explore multiparameter persistent homology challenges and potential solutions for extracting meaningful bar length statistics from complex topological data structures.

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

Optimal Reach Estimation

Discover optimal reach estimation techniques for embedded submanifolds, exploring minimax theory, curvature estimation, and statistical convergence rates in geometric data analysis.

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

Investigation of Data Clouds - From Galton's Ellipses to Explainable AI

Explore geometric approaches to statistical modeling from Galton's ellipses to explainable AI, introducing data molding concepts for unstructured big data analysis.

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

Modern Nonlinear Embedding Methods Unpacked

Uncover the theoretical foundations and practical improvements of t-SNE and UMAP embedding methods for high-dimensional data visualization and analysis.

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

Empirical Likelihood Methods for Fréchet Means on Open Books

Explore empirical likelihood methods for statistical inference on Fréchet means in open books, covering non-regular geometric behavior and Wilks's theorem applications.

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

Extrinsic and Intrinsic Manifold Learning - Old and New

Explore extrinsic and intrinsic manifold learning techniques, from testing manifold hypotheses in high-dimensional spaces to handling noisy distance data without embeddings.

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

The Probability of the Cut Locus of a Fréchet Mean

Explore advanced geometric probability theory through rigorous analysis of Fréchet means on Riemannian manifolds and their cut locus properties.

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

Data Integration Via Analysis of Manifolds - DIVAM

Explore advanced statistical methods for integrating diverse data types on manifolds, extending beyond traditional subspace analysis to handle complex geometric data structures.

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

Generalized Frechet Means with Random Minimizing Domains and Its Strong Consistency

Explore generalized Frechet means framework with random minimizing domains, covering strong consistency theorems and applications to non-Euclidean data analysis methods.

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

What is the Hodge Conjecture?

Discover the Hodge conjecture through Pierre Deligne's exploration of projective algebraic varieties, cohomology classes, and algebraic cycles in this Millennium Prize Problem lecture.

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