Notes
Although it is unlikely to be very useful to anyone at this stage, you can find my informal/in-progress notes wiki here. You can also find my even less organized math journal here.
Lectures and Courses
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K3 Surfaces (Phil Engel, Spring 2023)
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Hochschild Homology (Tekin Karadag, Spring 2023)
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Lie Algebras (Brian Boe, Fall 2022)
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Moduli Spaces (Valery Alexeev, Fall 2022)
Algebra
Representation Theory
Algebraic Geometry
Arithmetic Geometry and Number Theory
Topology
Analysis
Undergrad
Talks / Seminars / Mini Courses
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IAS/PCMI Graduate Summer School: Motivic Homotopy
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Combined Notes
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Danny Krashen, “Field arithmetic and the complexity of algebraic objects”
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Philippe Gille, “G-torsors over affine curves”
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Frédéric Déglise, “Motivic categories”
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Kirsten Wickelgren, “An introduction to $\AA^1$ homotopy theory using enumerative examples”
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Matthew Morrow, “Aspects of motivic cohomology”
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- Reading Seminar: Salamon-McDuff, “J-Holomorphic Curves and Symplectic Topology”
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Gromov-Witten invariants and regularity theorems:
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VRG notes on tilings and translation surfaces:
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Arizona Winter School, 2019
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Kirsten Wickelgren: A1 Enumerative Geometry
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Matthew Morrow: Topological Hochschild Homology in Arithmetic Geometry
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UCSD Algebraic Geometry Conference, 2019
Expository
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Classifying groups of order $pq$ using semidirect products: PDF
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An expository paper on the history of modern Algebraic Geometry (2017): PDF
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Some notes on the Math GRE:
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My math-related Twitter threads on Thread Reader.
Links to Notes by Others
Note: If you you write and share LaTeX notes, please let me know and I’d be happy to link your site here!
- Arun Debray maintains a page of lecture notes.
- Gilles Castel maintains a page of lecture notes .
- Evan Chen maintains a page of lecture notes, along with The Infinite Napkin.
- Dexter Chua has lecture notes from Cambridge courses.
- Aleksander Shmakov has some notes posted on his website.
- Anton Geraschenko has page of lecture notes.
- Chris Schommer-Pries has some lecture notes.
- Dongryul Kim has uploaded a large collection of live-tex’d notes from Harvard courses.
- Zoë Farmer has some notes from various undergraduate courses
- Akhil Matthew has some notes from graduate courses
- Henry Liu has notes from graduate courses
Resources / Remarks on Live-Texing
Some tools I use:
- I take notes using the neovim editor, manage them with the ranger file manager, and convert them to PDF/HTML with pandoc.
- My vim configuration is here.
- My entire notes respository is stored here.
- I keep a collection of pandoc templates and custom filters here.
- For diagrams:
- Inkscape for capturing freehand stylus drawings while live-texing.
- q.uiver for commutative diagrams in TikzCD.
- https://www.mathcha.io for converting hand-drawn stylus figures to Tikz code.
- QTikz/KTikz for plain Tikz or hand-edited TikzCD.
- For macros:
- I have several (very unorganized) files for Latex macros: a, b, c, d.
- I use a forked version of quicktex to automatically expand 2-3 letter shortcuts into full commands. My library of shortcuts is here.
- I use coc.nvim and coc-snippets to inline more complicated commands
- I use the iabbrev feature in neovim to automatically correct typos.
Some useful resources:
- I use the mathpix snipping tool to convert clips of images to tex, and their snip notes feature to convert entire PDFs or book pages.
- I keep loose research notes in Obsidian.
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The Gummi program has an excellent side-by-side view of tex and the PDF output which regularly updates after you’ve typed.
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Gilles Castel has a blog post describing live-texing with vim, along with another post about integrating Inkscape figures
- Chris Schommer-Pries has written a post on the Secret Blogging Seminar which includes some useful tips and tricks.