Harvard CMSA Courses

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

Quantum Exclusion Processes for and by Amateurs - Lecture 3

Dive into quantum exclusion processes with Denis Bernard, exploring fundamental concepts and applications accessible to beginners in this specialized field.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Crystal Skeletons

Explore the mathematical concept of Crystal Skeletons with Sylvie Corteel in this integrable systems program lecture from UC Berkeley.

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

The Equations of Generalised Hydrodynamics and Their Unusual Diffusive Corrections - Lecture 1

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 11 minutes
• Self-Paced
• Free Video

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

Entanglement Evolution and Quasiparticle Picture - Part 2

Delve into the entanglement evolution and quasiparticle picture with Pasquale Calabrese from SISSA Trieste, exploring integrable systems and their novel applications.

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

Random Fibonacci Words

Delve into the mathematical world of Fibonacci words, exploring coherent measures, clone Schur functions, and connections to total positivity, orthogonal polynomials, and stick-breaking models.

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

Integral Many-Body Systems and GHD - Lecture 3

Delve into Herbert Spohn's third lecture on integral many-body systems and Generalized Hydrodynamics (GHD) at Harvard CMSA's program on integrable systems.

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

Stochastic Heat Flow by Moments

Explore the Stochastic Heat Flow (SHF) as a scaling limit of directed polymers in random environments, focusing on a new axiomatic approach to prove uniqueness in law through the matching of moments.

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