Notes
I’ve typed up notes from classes that I’ve taken and short math programs (summer schools, conferences, etc.) that I’ve attended. You can read these free of charge, under the condition that all typos or errors be sent to me. As my note taking ability has improved over time, within each category these notes are listed in descending order of quality.
Conferences, Reading Groups
(Fall 2025) Banff Workshop on Singularities
These are notes from a workshop on Notions of Singularity in Different Characteristics [25w5409] at Banff Interational Research Station, held in October 2025. Much like my notes from the SRI bootcamp, these notes are incomplete and written mostly for my own use.
These are notes from the 2025 Summer Research Institute (SRI) in Algebraic Geometry, held at Colorado State University in July 2025. These notes are both hasty and incomplete, yet I suspect someone could find value in them.
(Fall 2024) Methods in Mixed Characteristic Geometry (MMCG)
These are notes from a Fall Course on geometry in mixed characteristic, held at Johannes Gutenberg University in Mainz, Germany in October 2024. The school was organized by Manuel Blickle, Karl Schwede, and Kevin Tucker. The main focus of this course was developing the p-adic Riemann Hilbert Correspondence and Prismatic Cohomology and applying them within algebraic geometry and commutative algebra. For suggested background and (far better) notes written by a subset of the speakers, see here.
(Fall 2023) Perfectoid Spaces (Mini-Course)
These are notes from a mini-course on Perfectoid Spaces taught by Kevin Tucker at UIC. This is meant to be a gentle and brief introduction that assumes as little background as possible. If the MMCG notes above are a bit too technical, maybe read these first.
(Summer 2023) MSRI/SLMath CMND Summer School
These are notes from the SLMath (formerly MSRI) summer school at the University of Notre Dame on Commutative Algebra and its Interaction with Algebraic Geometry.
Courses
(Spring 2023) Math 553: Algebraic Geometry II
This course covered chapters 2 and 3 of Hartshorne's book.
(Fall 2022) Math 520: Commutative Algebra
This is a good companion set of notes to the last time I took commutative algebra at the University of Michigan; this class is far more algebraic and results driven, whereas the former course was more geometric and computation driven.
(Fall 2022) Math 554: Complex Manifolds
While these notes are only for a bit more than half the course, they are organized and (relatively) consistent. These notes loosely follow Otto Forster's Lectures on Riemann Surfaces book.
(Fall 2019) Math 614: Commutative Algebra
This course was taught in an Inquiry Based Learning format. Attached are my solutions to the in-class exercises. More detailed course information can be found here.
(Winter 2019) Math 594: Graduate Algebra II
Groups, Fields, Representations, Galois Theory, and some Algebraic Number Theory.
(2015) AP US History (2014) AP World History
Send me an email if you or anyone you know actually found these useful!
How do I take these notes?
Many of these notes were Live-TeXed, though I personally do not recommend doing this and don’t do it anymore. I have found that I internalize information much better by writing it down then, at a later point, typing the notes to reinforce them (This is backed up by modern research!). The following tips, however, are still useful for speeding up your TeXing in general:
- Write Lots of Macros, and Use Them! Most people do this to some degree (e.g. use
\ZZinstead of\mathbb{Z}) but I would encourage using way more macros than this. Any time your instructor introduces notation, create a macro and toss it in your header file; I promise this makes typing go by much faster. You can also write some fun ones like\inv := ^{-1}or\recip := \frac{}; see (or steal) my header file for more examples of macros. - Use a Multimodal Editor. I use Neovim with Treesitter and Vimtex for syntax highlighting and autocomplete. Once you get comfortable using vim keybindings, you can navigate around a document like a pro and type down content much faster. It’s a steep learning curve, but don’t be discouraged!
- Use a Graphical Tool for TikZ Diagrams. Pretty self-explanatory, and most people do this anyway. Most people use Quiver, but I also like https://tikzcd.yichuanshen.de/.