Harvard CMSA Courses

Shalika Periods: Functoriality and Arithmetic

Delve into advanced mathematical concepts of Shalika periods, exploring their role in Langlands functoriality, automorphic descents, and applications to critical L-values of cuspidal automorphic forms.

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

Integrating Braided Categories Over 3-Manifolds

Delve into advanced mathematical concepts of factorization homology and braided-monoidal categories, exploring their applications in framed 3-manifolds and tangle hypothesis theory.

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

Tate's Thesis and P-adic Strings in Quantum Field Theory

Delve into p-adic string theory, exploring worldsheet actions, Tate's thesis, and their connection to quadratic reciprocity, with insights into Laplacian operators on Tate curves and Lorentzian developments.

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

Period Integrals of Automorphic Forms and the Residue Method

Delve into advanced mathematical concepts exploring period integrals of automorphic forms, focusing on the Jacquet-Rallis residue method and its applications to symplectic group studies.

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

LILO: Learning Interpretable Libraries by Compressing and Documenting Code

Discover how LILO framework combines LLM-guided synthesis with symbolic compression to create interpretable code libraries, enhancing program development through automated refactoring and documentation.

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

Fibered Ribbon Knots vs. Major 4D Conjectures - Part 1

Delve into advanced mathematical concepts exploring fibered ribbon knots, their relationship to smooth 4D Poincaré conjecture, and criteria for extending fibrations in topological studies.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

Fibered Ribbon Knots vs. Major 4D Conjectures - Part 2

Delve into advanced mathematical concepts exploring the slice-ribbon conjecture, fibered knots, and smooth disks in B^4, with insights on the (2,1)-cable of the figure eight knot.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes

Delve into advanced mathematical analysis of Kerr black hole stability, exploring axially symmetric perturbations and energy methods in general relativity through Maxwell and Einstein frameworks.

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

Factorization Algebras in Quite a Lot of Generality

Explore the mathematical framework of factorization algebras and their application to arithmetic geometry, examining world-structures and quantum field theory analogues in non-manifold contexts.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Computers and Mathematics in Partial Differential Equations - New Developments and Challenges

Explore how computers revolutionize mathematical proofs in partial differential equations, from traditional approaches to modern computer-assisted demonstrations and future possibilities.

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

Stretching and Shrinking - 85 Years of the Hopf Argument for Ergodicity

Delve into the mathematical foundations of ergodicity through Hopf's groundbreaking argument, exploring its applications in geometry, representation theory, and dynamics across 85 years of mathematical development.

• YouTube
• 1 hour 29 minutes
• Self-Paced
• Free Video

Characteristic Initial Value Problem for the 3D Compressible Euler Equations

Delve into advanced mathematical analysis of 3D compressible Euler equations, focusing on characteristic initial value problems, vectorfield methods, and Sobolev norm regularity theory.

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

Noncompact n-Dimensional Einstein Spaces as Attractors for the Einstein Flow

Delve into advanced mathematical analysis of Einstein flow dynamics, exploring how non-compact negative Einstein spaces behave under perturbations in n-dimensional contexts.

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

The Langlands Program via Arithmetic Quantum Field Theory - Talk 1

Dive into advanced mathematical concepts exploring the Langlands program through the lens of arithmetic quantum field theory, featuring expert insights on geometric formulations and boundary theories.

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

The Langlands Program via Arithmetic Quantum Field Theory - Talk 2

Delve into advanced mathematical concepts exploring the Langlands program through the lens of arithmetic quantum field theory with renowned mathematician David Ben-Zvi.

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