Harvard CMSA Courses

Locality and Smoothness of Quantum Field Theories

Explore locality and smoothness principles in quantum field theories through advanced mathematical frameworks and homotopy theory applications.

• YouTube
• 23 minutes
• On-Demand
• Free Video

SymTFT Approach for Non-Invertible Symmetries of Mixed States

Explore SymTFT approach for analyzing invertible and non-invertible symmetries in mixed quantum states through advanced topological field theory methods.

• YouTube
• 23 minutes
• On-Demand
• Free Video

Omega-Spectrum of Stabilizer Invertible Phases

Explore the mathematical framework connecting stabilizer invertible phases to omega-spectrum structures in quantum field theory and topological phases.

• YouTube
• 25 minutes
• On-Demand
• Free Video

The Classification of Two-Dimensional Extended Conformal Field Theories

Discover the mathematical classification of two-dimensional extended conformal field theories through advanced homotopy theory and operator algebra techniques.

• YouTube
• 23 minutes
• On-Demand
• Free Video

A Tour d'Horizon Through Homotopical Aspects of C*-Algebraic Quantum Spin Systems

Explore homotopy theory applications to quantum spin systems using C*-algebraic methods, covering state spaces, UHF algebras, and connections to topological phases of matter.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Finitely Correlated States Driven by Topological Dynamics

Explore finitely correlated quantum states through topological dynamics in this specialized mathematical physics presentation from Harvard CMSA's quantum field theory workshop.

• YouTube
• 20 minutes
• On-Demand
• Free Video

Introduction to Superselection Sector Theory - Classification of Phases and Long-Range Entanglement

Discover superselection sector theory for classifying quantum phases and understanding long-range entanglement in topological systems through mathematical frameworks.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Lattice Models and Topological Quantum Field Theories IV

Explore advanced connections between lattice models and topological quantum field theories in this specialized mathematical physics workshop session.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Local Definitions of Gapped Hamiltonians and Topological and Invertible States - IV

Explore advanced quantum field theory concepts through Kitaev's analysis of gapped Hamiltonians and topological states in this specialized workshop session.

• YouTube
• 1 hour 25 minutes
• On-Demand
• Free Video

Quantum Phase Diagrams - Order Parameters, Topological Invariants, Examples

Explore quantum lattice systems' ground states, phase diagrams, order parameters, and topological invariants through mathematical frameworks and concrete examples.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Defects as Functors Between Phases of Abelian Gauged Linear Sigma Models

Explore how defects function as functors between D-brane categories in Abelian gauged linear sigma models, with explicit construction methods for transporting branes across different phases.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Holography for Bulk-Boundary Local Topological Order

Explore holographic principles in quantum spin systems with topological boundaries, examining local topological order axioms and their applications to Levin-Wen and Walker-Wang models.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Tensor Network States - A Topological Field Theory Perspective

Explore tensor network states through topological field theory, connecting PEPS and MPO to Turaev-Viro models and categorical Morita theory for quantum many-body systems.

• YouTube
• 55 minutes
• On-Demand
• Free Video

p-form Puzzles - BF Theory and Electromagnetic Duality in Topological Field Theory

Explore p-form electrodynamics puzzles, BF theory equivalences, and electromagnetic duality connections to Ray-Singer torsion in topological field theory.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Non-Invertible Bosonic Chiral Symmetry on the Lattice

Explore non-invertible chiral symmetry construction on lattice systems, mimicking axial rotations in U(1) gauge theory with bosonic matter for quantum field theory applications.

• YouTube
• 51 minutes
• On-Demand
• Free Video