Harvard CMSA Courses

From Affine Hecke Category to Invariant Distributions

Delve into advanced mathematical concepts exploring affine Hecke categories, invariant distributions, and their applications in harmonic analysis through geometric realizations and Lusztig's asymptotic algebra.

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

Schubert Eisenstein Series and Poisson Summation for Schubert Varieties

Delve into advanced mathematical concepts exploring Schubert Eisenstein series, their meromorphic continuations, and connections to generalized Poisson summation formulas in arithmetic quantum field theory.

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

Automorphic Representations in String Amplitudes

Explore the connection between automorphic representations and string scattering amplitudes, focusing on wavefront sets, BPS conditions, and Fourier coefficient calculations in quantum field theory.

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

Statistics of Number Fields, Function Fields, and 3-Manifolds

Delve into advanced mathematical concepts exploring distributions of class groups across number fields, function fields, and fundamental groups in 3-manifolds, with insights on Cohen-Lenstra-Martinet conjectures.

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

Shtuka Special Cycles and Their Generating Series

Delve into advanced mathematical concepts exploring Shtuka special cycles, their generating series, and their applications in algebraic quantum field theory through expert insights from MIT's Wei Zhang.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Skein Algebras and Quantized Coulomb Branches

Explore the relationship between Kauffman bracket Skein algebra and quantized Coulomb branches in compact oriented surfaces, focusing on groundbreaking mathematical connections and theoretical frameworks.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

What 4-Graviton Scattering Amplitudes Had to Say About the Unitary Dual

Explore advanced concepts in unitary representations of Lie groups through the lens of 4-graviton scattering amplitudes, string theory, and E8 representations.

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

The Tame Categorical Local Langlands Correspondence

Delve into advanced mathematical concepts exploring the tame categorical local Langlands correspondence, focusing on p-adic groups and depth zero supercuspidal representations.

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

Objective-Driven AI: Towards AI Systems That Can Learn, Remember, Reason, and Plan

Explore groundbreaking concepts in AI development with Yann LeCun as he presents a modular cognitive architecture for machines to learn, reason, and plan like humans using predictive world models and H-JEPA.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

The Poisson Summation Conjecture and the Fiber Bundle Method - AQFT Lecture 3

Delve into advanced mathematical concepts exploring the Poisson summation conjecture, fiber bundle methods, and their applications to spherical varieties and L-functions in global fields.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

The Unknotting Number of a Knot - A Historical Perspective and Modern Developments

Explore the fascinating history and developments in understanding knot theory's unknotting number, from Tait's early work to modern 4-dimensional topology connections and remaining open questions.

• YouTube
• 1 hour 23 minutes
• Self-Paced
• Free Video

Solving Olympiad Geometry Without Human Demonstrations - AlphaGeometry's Automated Reasoning Approach

Discover how AlphaGeometry, a groundbreaking neuro-symbolic system, solves complex olympiad-level geometry problems by synthesizing millions of theorems and generating human-readable proofs without human demonstrations.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Recent Progress on Certain Problems Related to Local Arthur Packets of Classical Groups

Delve into recent mathematical advances concerning local Arthur packets of classical groups, wave front sets, and intersection problems in representation theory.

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

Covers of Reductive Groups and Functoriality in Local Field Theory

Delve into advanced mathematical concepts exploring covers of reductive groups, Langlands' functoriality principle, and their applications in local field theory and endoscopy.

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

Some Examples of the Relative Langlands Duality

Delve into advanced mathematical concepts of relative Langlands duality through real-world examples, exploring strongly tempered spherical varieties and trace formula comparisons.

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