|
David Penneys
Professor of Mathematics at The Ohio State University Office: Room 752 Math Tower Email: penneys (dot) 2 (at) osu (dot) edu |
|
Unitary Quantum Symmetries Lite
I am in the process of compiling my notes from 3 topics courses at OSU from 2018 (Quantum Algebra), 2021 (TOpological Phases of Matter), and 2023 (Higher Linear Algebra) into a book with Giovanni Ferrer and Kyle Kawagoe.
The book has 3 parts. Each part discusses objects, their endomorphisms, a weaker version of equivalence, some important examples, and applications.
I am in the process of compiling my notes from 3 topics courses at OSU from 2018 (Quantum Algebra), 2021 (TOpological Phases of Matter), and 2023 (Higher Linear Algebra) into a book with Giovanni Ferrer and Kyle Kawagoe.
The book has 3 parts. Each part discusses objects, their endomorphisms, a weaker version of equivalence, some important examples, and applications.
-
Part I: Hilb: Finite dimensional Hilbert spaces.
- Chapter 1: Hilbert spaces and operators
- Chapter 2: Operator algebras and their modules
- Chapter 3: Morita equivalence
- Chapter 4: The Temperley-Lieb-Jones algebras
- Chapter 5: Basic quantum information
- Chapter 6: Lattice models
- Part II: 2Hilb: Finite semisimple unitary categories.
- Part III: 3Hilb: Finite semisimple unitary 2-categories.
Files
Here are notes from my 2023 course on Higher Linear Algebra.
Here are notes from my 2023 course on Higher Linear Algebra.
- Motivational charts for the course
- Notes on finite dimensional Hilbert spaces and operator algebras
- Notes on (unitary) categories and 2-vector/Hilbert spaces
- Notes in progress on (unitary) tensor categories
- Notes in progress on (unitary) 2-categories
- Notes on finite dimensional operator algebras
- Notes on basic quantum information
- Notes on lattice models
- Notes on fusion categories
- Notes in progress on quantum constructions from unitary fusion categories
- Notes on unitary modular tensor categories
- Synoptic chart of tensor categories [animated video]
- Notes on 2-categories
- Notes on 3-categories
- Notes in progress on Phase transitions
- Quantum information meets quantum matter, Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen
- Topological Quantum Computation, Zhenghan Wang
- Topological Quantum: Lecture Notes and Proto-Book, Steven H. Simon
Announcements for UQSL
2024/4/24, 4:58
Updates coming soon!
Just getting the site up and running.
2024/4/24, 4:58
Updates coming soon!
Just getting the site up and running.
last modified: 2025/4/28