Harvard CMSA Courses

Entanglement Evolution and Quasiparticle Picture - Part 1

Explore the entanglement evolution and quasiparticle picture in integrable systems with Pasquale Calabrese from SISSA Trieste.

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

Integral Many-Body Systems and GHD - Lecture 2

Delve into integral many-body systems and Generalized Hydrodynamics (GHD) with Herbert Spohn in this advanced mathematical physics lecture from Harvard CMSA.

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

Large Time Cumulants of the Open KPZ Equation

Explore the mathematical analysis of large time cumulants in the open KPZ equation with Guillaume Barraquand from École normale supérieure de Paris.

• YouTube
• 1 hour 8 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

Quantum Exclusion Processes for (and by) Amateurs - Lecture 1

Explore quantum exclusion processes with Denis Bernard in this accessible lecture designed for beginners and enthusiasts alike.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

The Toda Lattice as a Soliton Gas

Delve into the Toda lattice as an integrable system, exploring how it behaves as a soliton gas under random initial data, with connections to random matrix theory and Lyapunov exponents.

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

Discovery in Mathematics with Automated Conjecturing

Explore the evolution of AI-driven mathematical discovery through automated conjecturing systems like TxGraffiti, GraphMind, and GraffitiAI, presented by Randy Davila of RelationalAI and Rice University.

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

AlphaProof: When Reinforcement Learning Meets Formal Mathematics

Dive into the intersection of reinforcement learning and formal mathematics with Thomas Hubert's exploration of AlphaProof, examining how machine intelligence and formal mathematics are transforming mathematical reasoning.

• YouTube
• 1 hour 26 minutes
• Self-Paced
• Free Video

Decoupling and Decay of Two-Point Functions in a Two-Species TASEP

Explore the decoupling and decay of two-point functions in a two-species TASEP with Patrik Ferrari from Universität Bonn, part of Harvard CMSA's program on integrable systems.

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

Multispecies ASEP and t-PushTASEP on a Ring and a Strange Five Vertex Model - Lecture 1

Explore Atsuo Kuniba's lecture on multispecies ASEP, t-PushTASEP on a ring, and a strange five vertex model in integrable systems theory.

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

Unstable Fluids in Expanding Cosmologies

Explore numerical evidence for instabilities in non-linearly perturbed FLRW cosmological models, including Rendall's conjecture on super-radiative equations of state and shock formation in slowly expanding universes.

• YouTube
• 56 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