Harvard CMSA Courses

Datasets for Math: From AIMO Competitions to Math Copilots for Research

Explore the evolution of mathematical datasets from AIMO competitions to research copilots, examining limitations, proposing structural shifts, and discussing how LLMs are redefining mathematical evaluation.

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

Cosmology and Cosmological Polytopes I

Explore the intersection of cosmology and mathematical polytopes in this advanced physics lecture by renowned theoretical physicist Nima Arkani-Hamed.

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

Positive Grassmannian and Cluster Algebras I

Explore the mathematical foundations of positive Grassmannian varieties and their deep connections to cluster algebra structures in this advanced lecture.

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

Lightning Talks - Total Positivity and Quantum Field Theory

Explore cutting-edge research in total positivity and quantum field theory through rapid-fire presentations on amplituhedron limits, kinematic stratifications, and P-matrix geometry.

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

Scattering Amplitudes and Amplituhedra II

Explore advanced concepts in scattering amplitudes and amplituhedra geometry with expert insights into quantum field theory applications.

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

Positive Grassmannian and Cluster Algebras III

Explore advanced connections between positive Grassmannian varieties and cluster algebras in this specialized mathematical lecture from Harvard CMSA's summer school.

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

Positive Geometry of Polypols

Explore the mathematical foundations of positive geometry applied to polypols in this advanced mathematical physics lecture from Harvard CMSA's summer school series.

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

Cosmology and Cosmological Polytopes II

Explore advanced cosmological polytopes and their geometric structures in quantum field theory with renowned physicist Nima Arkani-Hamed in this specialized lecture.

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

Positive Grassmannian and Cluster Algebras II

Explore advanced connections between positive Grassmannian geometry and cluster algebra structures in this specialized mathematical lecture from Harvard CMSA's summer school series.

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

Cosmology and Cosmological Polytopes III

Explore advanced cosmological polytopes and their applications in quantum field theory through cutting-edge mathematical frameworks and theoretical physics insights.

• YouTube
• 1 hour 37 minutes
• Self-Paced
• Free Video

Definitions and First Examples of Positive Geometries II

Explore fundamental concepts and initial examples of positive geometries in this advanced mathematical framework connecting total positivity with quantum field theory applications.

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

Scattering Amplitudes and Amplituhedra III

Explore advanced geometric structures in quantum field theory through amplituhedra and their connection to scattering amplitude calculations.

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

Scattering Amplitudes and Amplituhedra I

Discover the geometric foundations of scattering amplitudes through amplituhedra, exploring how positive geometry revolutionizes quantum field theory calculations.

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

Positive Geometry of Polytopes

Explore the mathematical foundations of positive geometry through polytopes and their applications in quantum field theory and total positivity.

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

Can Transformers Reason Logically? A Study in SAT-Solving

Explore how Transformer models perform Boolean reasoning and solve 3-SAT problems, examining their capabilities, limitations, and potential solutions through Chain-of-Thought methodology and DPLL algorithms.

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