Harvard CMSA Courses

Datasets for Math: From AIMO Competitions to Math Copilots for Research

Explore the evolution of mathematical datasets from AIMO competitions to research copilots, examining limitations, proposing structural shifts, and discussing how LLMs are redefining mathematical evaluation.

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

Orthogonality of Spin q-Whittaker Polynomials

Delve into the orthogonality of spin q-Whittaker polynomials, exploring their properties as symmetric polynomials, eigenrelations, and applications to directed random polymer models with Beta weights.

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

Symmetries of Periodic and Free Boundary Measures on Partitions

Explore the hidden distributional symmetry in periodic and free boundary q-Whittaker measures on partitions, including parameter exchanges and related Hall-Littlewood measures results.

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

Pfaffian Point Process for TASEP on the Half Line - Part 3

Delve into the Pfaffian point process for TASEP on the half line, exploring integrable systems with Jan De Gier from University of Melbourne.

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

Monitored Quantum Systems, Product of Random Matrices and Permutations

Explore the connections between monitored quantum systems, random matrix products, and permutations in this mathematical physics lecture by Andrea De Luca.

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

Ramanujan Property and Edge Universality of Random Regular Graphs

Explore the spectral properties of random d-regular graphs, focusing on eigenvalue rigidity and edge universality, and discover how these concepts relate to Ramanujan graphs and the Tracy-Widom distribution.

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

Multinomial Dimers and 3D Limit Shapes

Explore the multinomial dimer model on graphs, including partition function formulas and 3D limit shapes in the Aztec Diamond, based on Richard Kenyon's research with Catherine Wolfram.

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

Pfaffian Point Process for TASEP on the Half Line - Lecture 2 of 3

Explore the Pfaffian point process for TASEP on the half line in this advanced mathematical lecture by Jan De Gier, part of a series on integrable systems.

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

Random Partitions at High Temperature

Explore discrete particle ensembles and random partitions at high temperature, examining limiting measures and Markov chains through Jack symmetric polynomials and Fourier transforms.

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

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

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