Harvard CMSA Courses

Geometric Transition from Maximal SYM to ABJM Theory

Explore the geometric transition between theoretical models, focusing on ABJM amplituhedron construction, symplectic reduction, and positivity conditions in quantum field theories.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Introduction to Cluster Algebras

Explore the foundations of cluster algebras, their combinatorial structures, and connections to mathematics and physics, including positivity theory and Grassmannian coordinate rings.

• YouTube
• 45 minutes
• On-Demand
• Free Video

Scattering Amplitudes and Cluster Algebras

Explore the intricate relationship between cluster algebras and scattering amplitudes in N=4 super Yang-Mills theory, focusing on 6 and 7 particle cases and their Grassmannian structures.

• YouTube
• 47 minutes
• On-Demand
• Free Video

U-Equations from Finite Dimensional Algebras - Applications in Cluster Algebras and Amplitudes

Explore finite dimensional algebra systems and their applications in representation theory, focusing on u-equations, tau-tilting theory, and connections to cluster algebras and amplitudes.

• YouTube
• 51 minutes
• On-Demand
• Free Video

The Magic Number for the M=2 Amplituhedron

Delve into advanced mathematical concepts exploring amplituhedron tilings, focusing on the m=2 case and its consistent cardinality properties across different configurations.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Chambers and All Loop Geometry for Four-Point Correlators in N=4 SYM Theory

Delve into advanced theoretical physics concepts exploring loop geometry, amplituhedron, and four-point correlators in N=4 SYM theory, with focus on chamber forms and loop fibration.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Amplituhedron - From Positive Grassmannian to Scattering Amplitudes

Dive into the mathematical foundations of Amplituhedron, exploring its relationship with positive Grassmannian geometry and scattering amplitudes in theoretical physics through expert insights.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

All-Order Splits and Multi-Soft Limits for Particle and String Amplitudes

Delve into advanced particle physics concepts, exploring split factorizations, binary geometry, and multi-soft limits in scattering amplitudes across various theoretical frameworks.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Introduction to Affine Cluster Algebras

Delve into affine cluster algebras, exploring their infinite clusters, mutation sequences, and connections to finite cluster algebras and N=4 SYM amplitude calculations in particle physics.

• YouTube
• 52 minutes
• On-Demand
• Free Video

The Chow-Lam Form for Subvarieties of Grassmannian

Dive into advanced mathematical concepts exploring the Chow-Lam form, its relationship to projective varieties, and its applications in studying amplituhedra through universal projection formulas.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Combinatorics of m=1 Grasstopes

Explore the mathematical foundations of Grasstopes, focusing on their combinatorial properties, geometric relationships with amplituhedra, and applications in calculating scattering amplitudes in physics.

• YouTube
• 43 minutes
• On-Demand
• Free Video

Introductory Lecture on Positive Geometries

Dive into the fundamental concepts of positive geometries, exploring their role in scattering amplitudes, polytopes, and flag varieties through an accessible mathematical framework.

• YouTube
• 55 minutes
• On-Demand
• Free Video

The Tropical Amplituhedron - Structure and Boundaries in Quantum Field Theory

Explore the groundbreaking tropical amplituhedron concept and its role in quantum field theory calculations, focusing on its structure, boundaries, and relationship to positive Grassmannian.

• YouTube
• 22 minutes
• On-Demand
• Free Video

Corks for Exotic Diffeomorphisms in 4-Manifolds

Delve into advanced topology concepts exploring exotic smooth structures, cork twists, and diffeomorphisms in 4-manifolds, with applications to contemporary mathematical research.

• YouTube
• 53 minutes
• On-Demand
• Free Video

Can Embedding Problems Be Used to Distinguish S^4 from Other Homotopy 4-Spheres?

Delve into advanced topology concepts exploring embedding problems, 4-spheres, and 3-manifold theory through Heegaard diagrams and their applications in distinguishing homotopy 4-spheres.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video