Harvard CMSA Courses

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

An AI Approach to a Conjecture of Erdős

Explore how machine learning tackles Erdős' conjecture on tree independence sequences, uncovering thousands of counterexamples using PatternBoost architecture.

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

Predicting Euler Factors of Elliptic Curves

Discover how machine learning models predict Euler factors of elliptic curves with surprising accuracy from limited data in this advanced mathematical research presentation.

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

Machine Learning Mutation-Acyclicity of Quivers

Explore machine learning approaches to determining mutation-acyclicity properties in quiver theory through advanced mathematical techniques.

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

Recent Developments in Automated Conjecturing

Explore how machines generate mathematical conjectures using optimization, enumeration, and AI, from graph theory to string theory with automated verification in Lean 4.

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

BKL Bounces Outside Homogeneity

Delve into Warren Li's exploration of BKL bounces in General Relativity, examining how spacetime dynamics near singularities decouple and follow chaotic patterns, with proof of decoupling even with spatial inhomogeneity.

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

Positive Scalar Curvature with Point Singularities

Delve into topological constructions of positive scalar curvature metrics with uniformly Euclidean point singularities, challenging Schoen's conjecture and exploring geometric flow limitations.

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

Machine Learning G2 Geometry

Delve into machine learning applications for G2 geometry in string and M-theory, exploring how neural networks can learn topological properties and metrics of holonomy G2 manifolds for advanced mathematical physics research.

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

Symmetry Operators and Gravity in Quantum Theory

Delve into advanced theoretical physics concepts examining the relationship between symmetry operators and gravity, focusing on topological operators and the challenges of conserved charges in gravitational theory.

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

Some Aspects of Symmetry Descent in Quantum Field Theories

Delve into the relationship between Quantum Field Theories and string geometry through SymTFTs, exploring symmetry structures and their geometric engineering applications.

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

Symmetries in Quantum Field Theory and Gravity

Dive into advanced concepts of symmetries and their crucial role in quantum field theory and gravitational physics, exploring fundamental principles and theoretical frameworks.

• YouTube
• 1 hour 35 minutes
• Self-Paced
• Free Video

Conserved Charges of Closed Universes

Delve into quantum gravity's conserved charges, exploring their role in closed universes and discovering how ensemble holography connects to fundamental symmetry principles.

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

Aspects of Categorical Symmetries for Branes

Explore advanced mathematical concepts in categorical symmetries and their applications to brane theory, focusing on cutting-edge developments in theoretical physics and geometry.

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

Non-Invertible Symmetries, Generalized Gauging and Factorization

Explore advanced concepts in holography through analysis of 2d RCFTs, examining symmetries, gauging operations, and factorization in multi-boundary geometries.

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

S-Matrix Bootstrap and Black Hole Production

Explore the theoretical physics of black hole production in scattering amplitudes, examining symmetry-breaking effects and elastic amplitudes through S-matrix bootstrap methodology.

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