Harvard CMSA Courses

Transformers Meet Lyapunov - What Does It Take to Solve a Hard Math Problem?

Explore how transformers and Lyapunov theory intersect in solving complex mathematical problems, with insights from Meta AI's research on neural networks and mathematical reasoning.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Conceptual Challenges in Modern AI

Explore modern AI's conceptual challenges through Meta AI researcher Leon Bottou's analysis of mathematical foundations and current limitations in machine learning systems.

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

Case Studies in Reinforcement Learning

Explore reinforcement learning principles through real-world case studies, examining mathematical foundations and practical applications in machine learning optimization and decision-making.

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

Overview of AI for Mathematics

Explore how artificial intelligence intersects with mathematical research, from foundational concepts to cutting-edge applications in computational problem-solving and theorem proving.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

Theory of Machine Learning

Explore fundamental mathematical principles underlying machine learning, neural networks, and deep learning architectures with Princeton researcher Boris Hanin's comprehensive theoretical analysis.

• YouTube
• 1 hour 25 minutes
• Self-Paced
• Free Video

Symbol Alphabets from Tensor Diagrams in Yang-Mills Theory

Explore tensor diagrams and their connection to symbol alphabets in particle amplitudes, focusing on web series evaluation and polytope analysis in Yang-Mills theory.

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

Loops in a Loop Expansion - A Framework for Negative Geometries

Delve into advanced quantum field theory concepts, exploring loop expansions in N=4 SYM theory, amplituhedron construction, and differential equation methods for calculating integrated expressions.

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

Minimal Kinematics on M₀,n and Beyond

Explore the intersection of Minimal and Planar Kinematics in moduli spaces, examining critical points through rational formulas and their connection to polytopes and CEGM amplitudes.

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

Cosmological Polytopes and Beyond - From Bunch-Davies Wavefunctions to Optical Polytopes

Explore fundamental physics through cosmological polytopes, examining Bunch-Davies wavefunctions and their role in scalar theories, optical polytopes, and weighted geometries.

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

Cluster Algebras and Tilings of Amplituhedra

Explore the mathematical connections between cluster algebras and amplituhedra tilings, focusing on BCFW tilings and their relationship to Grassmannian structures in physics.

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

Surface Kinematics and the All-Loop Integrand for Gluon Amplitudes

Dive into advanced theoretical physics as Nima Arkani-Hamed explores surface kinematics and gluon amplitude integrands, examining cutting-edge developments in quantum field theory and particle physics.

• YouTube
• 1 hour 25 minutes
• Self-Paced
• Free Video

Scattering Amplitudes, Positive Geometry and the Amplituhedron

Delve into advanced quantum field theory concepts, exploring scattering amplitudes, positive geometry, and amplituhedron in N=4 super Yang-Mills theory with focus on Grassmannian cluster algebras.

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

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video