Harvard CMSA Courses

Moduli Spaces of 4D N=2 Quantum Field Theories

Explore the geometric structures of 4d N=2 quantum field theories through their moduli spaces, focusing on Coulomb branch geometry and algebraic integrable systems.

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

Tropicalized Quantum Field Theory

Discover a revolutionary approach to quantum field theory computations using tropicalization, enabling polynomial-time algorithms for previously intractable perturbative calculations.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Special Kähler Geometry and Collapsing

Explore special Kähler geometry's role in supersymmetric gauge theories and mirror symmetry, focusing on hyperkähler manifolds with algebraic integrable systems and metric collapse.

• YouTube
• 1 hour 17 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

Spontaneous Kolmogorov-Arnold Geometry in Vanilla Fully-Connected Neural Networks

Explore how Kolmogorov-Arnold geometry spontaneously emerges in standard neural networks through training, revealing distinctive geometric patterns in shallow MLPs.

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

Math for AI and AI for Math - Geometric and Symbolic Perspectives

Explore the geometric foundations of machine learning and discover how AI can advance pure mathematics through abstraction, decomposition, and formalization insights.

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

Ricci Flow as a Test for AI

Explore how Ricci flow from differential geometry can serve as a challenging benchmark for testing artificial intelligence capabilities in advanced mathematics.

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

Gauss - Towards Autoformalization for the Working Mathematician

Discover how Gauss, a new AI agent, assists mathematicians in formal proof writing, featuring a breakthrough Lean proof of the Prime Number Theorem for non-coding researchers.

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

FrontierMath to Infinity - Mathematical Problem Solving Benchmark and AI Trajectory

Explore FrontierMath benchmark design and AI's mathematical problem-solving trajectory, plus speculation on perfectly efficient mathematical intelligence capabilities.

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

The Shape of Math to Come

Explore ongoing experiments that may reshape research mathematics within the next decade through insights from cutting-edge mathematical research and emerging methodologies.

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

Topological Analysis of Spiking Correlation Networks in Neurological Systems

Explore topological analysis methods for spiking neural networks, examining brain organoid connectivity patterns and network resilience through manifold hypothesis applications.

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

Self-Supervised Learning, JEPA, World Models, and the Future of AI

Discover cutting-edge AI concepts including self-supervised learning, JEPA architecture, and world models from renowned expert Yann LeCun in this Harvard lecture.

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

How to Think About the Shape of Mathematics

Explore mathematical structures through geometric perspectives and discover how spatial thinking transforms abstract mathematical concepts into intuitive frameworks.

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

Symmetries and Moduli Spaces - Baby Steps beyond Calabi-Yau

Explore the interplay between symmetries and moduli spaces in string compactifications, moving beyond Calabi-Yau to G_2 and Spin(7) cases with worldsheet anomalies and non-invertible symmetries.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video