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 available to the public. 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 Warning: these notes are not peer-reviewed.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