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 compiled here, or accessible piecemeal here.
Lectures and Courses
Arithmetic Geometry and Number Theory
Algebraic Number Theory
Algebraic Curves
Étale Cohomology
Rational Points
Algebraic Geometry
Algebraic Geometry
Moduli Spaces
4-Manifolds and Algebraic Surfaces
Stacks and Moduli
Representation Theory
Algebraic Groups
Flag Varieties, Equivariant Cohomology, and K Theory
Topology
Floer Homology
Characteristic Classes
Algebra
Homological Algebra
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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A note on motivating and using semidirect products to classifying finite groups: PDF
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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
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.
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