Harvard CMSA Courses

3D Mirror Symmetry is 2D Mirror Symmetry

Delve into the mathematical connections between 3D and 2D mirror symmetry, exploring SYZ-type transforms and the exchange of Kähler and equivariant parameters in this advanced algebraic geometry seminar.

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

How Much Math Is Knowable?

Explore the boundaries of mathematical knowledge with Scott Aaronson as he delves into theoretical computer science, from Gödel's Incompleteness Theorem to quantum computing and beyond.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Hyperbolic Equations in a Double Null Gauge

Explore the hyperbolic nature of Einstein equations in a double null gauge, focusing on its advantages for quantitative analysis, including reducing equations to ODEs along null curves and Bianchi equations to first-order hyperbolic systems.

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

On Integrable Quantum and Classical Circuits with Stochastic Boundaries - Lecture 1 of 3

Explore Yang-Baxter integrable brickwork quantum circuit models, their integrability structure, and connections to KPZ scaling at the isotropic point, plus related classical integrable Landau-Lifshitz circuits.

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

Solutions of Tetrahedron and 3D Reflection Equations from Quantum Cluster Algebras - Lecture 2

Explore how quantum cluster algebras generate solutions to tetrahedron and 3D reflection equations, generalizing and unifying known approaches in this advanced mathematical lecture.

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

The Equations of Generalised Hydrodynamics and Their Unusual Diffusive Corrections - Lecture 2

Delve into the hydrodynamics of one-dimensional integrable models, exploring generalised hydrodynamics equations, their properties, and the unusual diffusive corrections governed by long-range correlations rather than standard derivative expansions.

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

Extremal Particles in Uniform Random Gelfand-Tsetlin Patterns - Lecture 1

Explore edge fluctuations in uniform random interlacing patterns with fixed top configuration, examining limit processes and conditions for their occurrence in Gelfand-Tsetlin patterns.

• YouTube
• 1 hour 2 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