Harvard CMSA Courses

Random Solitons and Soliton Gas

Explore the behavior of solitons in nonlinear dispersive equations, focusing on Korteweg de Vries equation, soliton gas formation as N approaches infinity, and statistical properties of random soliton solutions.

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

How Yang-Baxter Unravels Kardar-Parisi-Zhang

Delve into the mathematical exploration of Kardar-Parisi-Zhang class of stochastically growing interfaces, examining how the Yang-Baxter equation provides a foundational approach to proving universal scaling limits.

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

Positive Mass Theorem for ALE(AE) and ALF(AF) Toric 4-Manifolds

Delve into the positive mass theorem for toric 4-manifolds, exploring refinements to this fundamental conjecture in mathematical relativity and examining proofs that extend to higher dimensions with additional assumptions.

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

Exact Density Profile and Current Fluctuations in a Tight-Binding Chain with Dephasing Noise

Delve into the exact analysis of density profiles and current fluctuations in tight-binding chains with dephasing noise, exploring quantum master equations and Bethe ansatz techniques.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Integral Many-Body Systems and GHD

Explore integral many-body systems and Generalized Hydrodynamics (GHD) with Herbert Spohn from Technische Universitaet Muenchen in this advanced physics lecture.

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

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

Explore quantum integrability in many-body quantum Markov chain generators, focusing on XX model with dephasing noise and its mapping to Hubbard model with imaginary interaction in both Hamiltonian and circuit formulations.

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

Approach to Stationarity for KPZ Fluctuations in Finite Volume

Delve into the mathematical analysis of KPZ fluctuations in finite volume, exploring approaches to compute cumulants of height through asymmetric exclusion processes, matrix product representations, and Bethe ansatz methods.

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

On Integrable Quantum and Classical Circuits with Stochastic Boundaries

Explore matrix product solutions for quantum many-body Markov chains in Yang-Baxter integrable quantum circuits with stochastic boundaries, including applications to XXZ and Hubbard chain systems.

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

Box-Ball Systems - Lecture 3

Explore the evolution of box-ball systems, integrable cellular automata, through ultradiscretization, quantum group crystal theory, Bethe ansatz, and generalized hydrodynamics.

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

Low-regularity Local Well-posedness of the Elastic Wave System

Delve into the local well-posedness of elastic wave systems in 3D, exploring how admissible harmonic elastic materials split into divergence and curl parts with distinct quasilinear wave systems and optimal Sobolev norm conditions.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Learning Dynamical Transport without Data

Explore dynamical transport algorithms for generative modeling without data, focusing on sampling from target distributions using unnormalized log-likelihood functions, with applications in physics, chemistry, and Bayesian inference.

• YouTube
• 49 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