Harvard CMSA Courses

Building the Braided Fusion Category of Superselection Sectors I

Explore superselection sector theory and learn to construct braided fusion categories in quantum field theory through rigorous mathematical foundations.

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

Local Definitions of Gapped Hamiltonians and Topological and Invertible States II

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

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

Quantum Lattice Systems - Observables, Dynamics, Ground States, and GNS Representation

Explore quantum lattice systems fundamentals including observables, dynamics, ground states, GNS representation, and ground state gap with practical examples.

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

Lattice Models and Topological Quantum Field Theories II

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

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

Introduction to Superselection Sector Theory - Motivation and Basic Setting

Discover the fundamental principles of superselection sector theory and its basic mathematical framework in quantum field theory applications.

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

Local Definitions of Gapped Hamiltonians and Topological and Invertible States I

Explore local definitions of gapped Hamiltonians and topological states with quantum field theory expert Alexei Kitaev from Caltech in this advanced physics workshop.

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

Mapping the Landscape of Frustration-Free Models

Explore the mathematical landscape connecting frustration-free quantum models to hereditary subalgebras and open projections in operator theory.

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

A Categorification of Quinn's Finite Total Homotopy TQFT with Application to TQFTs and Once-Extended TQFTs Derived from Discrete Higher Gauge Theory

Explore advanced categorification of Quinn's finite total homotopy TQFT, extending to once-extended versions using groupoids and linear profunctors for discrete higher gauge theory applications.

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

On the Categorical Spectrum of Topological Quantum Field Theories

Explore the categorical spectrum framework for topological quantum field theories, connecting invertible TQFTs to generalized homology theory and anomaly boundaries.

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

An Algebraic Theory of Planon-Only Fracton Orders

Explore an algebraic framework for planon-only abelian fracton orders in 3D quantum phases, focusing on fusion, statistics, and classification of restricted particle excitations.

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

Some Thoughts About the Kapustin-Kitaev Cobordism Conjecture

Explore advanced mathematical physics connecting gapped quantum phases to bordism theory, investigating the Kapustin-Kitaev conjecture through category theory and topological methods.

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

Generalized Kitaev Pairings and Higher Berry Curvature in Coarse Geometry

Explore advanced mathematical concepts connecting Kitaev pairings with coarse geometry, extending topological invariants to higher dimensions and Berry curvature theory.

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

Quantizing Homotopy Types

Explore advanced topological quantum field theory through Kontsevich's quantization of finite homotopy types and its enhancement to fully extended TQFTs in iterated algebras.

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

Moduli Spaces of Projective 3D TQFTs

Explore moduli spaces of 3D topological quantum field theories and their connection to gapped quantum systems through homotopy theory and ribbon category automorphisms.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Mathematical Puzzles from the Entanglement Bootstrap - On Immersions and Regular Homotopy

Explore mathematical puzzles arising from entanglement bootstrap theory, focusing on immersions and regular homotopy in quantum field theory applications.

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