Harvard CMSA Courses

The Quantum GIT Conjecture in Fano Varieties and G-Actions

Delve into advanced mathematical concepts exploring the Quantum GIT conjecture, focusing on Fano varieties, equivariant quantum cohomology, and Hamiltonian G-manifolds in algebraic geometry.

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

Tyurin Degenerations, Relative Lagrangian Foliations and DT Invariant Categorification

Delve into advanced mathematical concepts exploring Tyurin degenerations, derived Lagrangian intersection theory, and categorification of DT invariants in Calabi-Yau threefolds.

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

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

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

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

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