Notes and Write ups

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, these notes are also listed in descending order of quality.

The most recent notes have all been written using the neovim text editor and the latexmk compiler. These interface using the plugin VimTeX with Treesitter for syntax highlighting and autocomplete. I render my PDFs using sioyek, which was designed specifically for academic papers and integrates seamlessly with the above tools. I strongly recommend it for reading papers as well as compiling them; an overview of its striking capabilities (smart linking, annotations, highlights, reverse search, etc.) can be found in the documentation.

University of Illinois, Chicago

(Fall '24) Methods in Mixed Characteristic Geometry (MMCG) 2024 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. For my live-TeXed notes, see here.

(Fall '23) 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. The notes can be found here. If the MMCG notes above are a bit too technical, maybe read these first.

(Summer '23) MSRI/SLMath CMND Summer School 2023 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. The notes can be found here.

(Spring '23) Math 553: Algebraic Geometry II This course covered chapters 2-3 of Hartshorne's book. The notes can be found here.

(Fall '22) 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. The notes for this course can be found here.

(Fall '22) 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. The link to them can be found here.

University of Michigan

(Fall '19) Math 614: Commutative Algebra More detailed course information can be found here. The (mostly complete) solutions to the in class IBLs can be found here.

(Winter '19) Math 594: Graduate Algebra II Groups, Fields, Representations, Galois Theory, and some Algebraic Number Theory. More detailed course information can be found here. (Mostly finished) TeXed notes can be found here.

High School

(2015) AP US History Notes summarizing all the material for the AP Exam can be found here.

(2014) AP World History Notes summarizing all the material for the AP Exam can be found here.

Non-Academic

(2025) I wrote a short-to-medium piece (for my own sake) on the Digital Revolution and a Case for Optimism. We live in challenging times, and now more than ever, I think that a positive outlook is not only warranted, but necessary. To read more, click here. Comments welcome!

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