Harvard CMSA Courses

Symmetries in the Hilbert Bundle Formulation of Quantum Gravity

Delve into quantum gravity's hydrodynamic approximation, exploring Einstein's equations, Hilbert bundles, and their relationship to spacetime symmetries through advanced mathematical frameworks.

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

Global Aspects of Exactly Marginal Current-Current Deformations

Delve into advanced theoretical physics concepts exploring conformal field theories, current-current deformations, and their relationship to discrete gauging and symmetry transformations in two dimensions.

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

Gravity and Bootstrap in Quantum Field Theory

Delve into advanced concepts of gravitational physics and bootstrap methods, exploring theoretical frameworks and their applications in modern physics research with expert Leonardo Rastelli.

• YouTube
• 1 hour 32 minutes
• Self-Paced
• Free Video

Expanders from Local to Global - Understanding Network Connectivity and High Dimensional Expanders

Explore the mathematical world of expander graphs and high-dimensional expanders, from fundamental concepts to advanced applications in network theory, error correction, and theoretical computer science.

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

Stability and Instability of Relativistic Fluids in Slowly Expanding Spacetimes

Explore the stability dynamics of relativistic fluids across expanding spacetimes, examining phase transitions between stable and unstable states in FLRW models with varying expansion rates.

• YouTube
• 1 hour 2 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

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

From Superspace to Twisted Supergravity

Delve into a geometric perspective on pure spinor superfield formalism and its applications to twisted supergravity, exploring homotopy Poisson–Chern–Simons theories and supergeometric origins.

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

Resurgence, Number Theory, and Quantum Mirror Curves

Delve into resurgence theory's application in quantum physics, exploring how non-perturbative data reveals number-theoretic properties in quantum mirror curves and toric Calabi-Yau threefolds.

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

Integrability in Discrete Random Matrix Theory

Explore integrability in discrete random matrix theory, covering probabilistic results, Hall-Littlewood polynomial formulas, and new formulas for Hermitian and antisymmetric p-adic matrices with formal Hall-Littlewood processes.

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

Unveiling the Classical Integrable Structure of Weak Noise Theory of KPZ Class

Delve into the classical integrable structure of weak noise theory in KPZ class, exploring the matrix Log-Gamma polymer and q-TASEP with Alexandre Krajenbrink.

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