**Under construction!**

Over the past several years, I’ve written (or want to write) several expository notes. Unfortunately, many of them are incomplete and inaccurate. I will try to upload them as soon as possible so that they can be made publicly available in case they may be useful. Many of these notes were written just so that I could better understand the topic. Some of these are also lecture notes that I wrote for talks that I’ve given. Warning: these notes are not peer-reviewed. Any errors contained in these documents are due to me and not my references. Unfortunately, I have occasionally not listed my references in some of the files, so I try to write them here.

Physics

- Quantum causal histories (coming soon)
- The Berry phase (reference: Brian Hall,
*Quantum Theory for Mathematicians*. GTM, Springer-Verlag New York 2013) - The Brillouin torus
- The renormalization group in condensed matter (with Steven Vayl)
- Kruskel-Szekeres coordinates and Penrose diagrams
- Scratch notes on quantum mechanics (unfinished)

Mathematics

- Baez-Fritz-Leinster’s theorem on entropy
- Fadeev’s theorem on entropy
- Notes on 2-categories
- Group cohomology and Kac-Moody groups (Unfinished)
- The Gelfand-Naimark Theorem (updated Jan 2016)
- Homotopy theory for Physicists (some notes prepared for the CCNY Journal club)
- Universal homotopy theories (reference: Daniel Dugger, “Universal homotopy theories.”
*Advances in Mathematics*, Vol 164, Issue 1, 2001, pp 144-176) - On spectra and cohomology theories
- The simplicial nerve and examples
- Postnikov systems, Whitehead towers, and gerbes (expanded version of one talk given at the Student Algebraic Topology Seminar in Fall 2014)
- Simplicial sets following mainly Goerss and Jardine’s book (two talks given at the Student Algebraic Topology Seminar in Fall 2014)
- What is a 2-sheaf/1-stack?
- From Lie 2-groups to Lie 2-algebras