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

Read More

Galois Cohomology and Class Field Theory

Pete Clark, Spring 2021

Read More

Algebraic Geometry

Algebraic Geometry

Read More

4-Manifolds and Algebraic Surfaces

Read More

Representation Theory

Lie Algebras

Chun-Ju Lai, Fall 2019

PDF

Read More

Category $\OO$

Brian Boe, Spring 2020

PDF V2, HTML V2

Read More

Categorification

Arik Wilbert, Summer 2020

PDF HTML

Read More

Flag Varieties, Equivariant Cohomology, and K Theory

Read More

Topology

Algebraic Topology

Justin Roberts, Fall 2017 and Spring 2018

PDF, HTML

Read More

Morse Theory

Akram Alishahi, Spring 2020

PDF

Read More

Floer Homology

Read More

Characteristic Classes

Read More

Algebra

Abstract Algebra

Dan Nakano, Fall 2019

PDF, HTML

Read More

Commutative Algebra

Pete Clark, Spring 2020

PDF

Read More

Homological Algebra

Read More

Analysis

Real Analysis

Neil Lyall, Fall 2019

PDF

Read More

Complex Analysis

Jingzhi Tie, Spring 2020

PDF, HTML

Read More

Undergrad

Undergraduate Compendium

A giant study guide of undergraduate topics I wrote while studying for the Mathematics Subject GRE.

(Self study, Spring 2017)

PDF, HTML

Read More

Combinatorics

A study guide for undergraduate Combinatorics.

PDF, HTML

Read More

Smooth Manifolds

Notes on Lee’s smooth manifolds.

PDF, HTML

Read More

Talks / Seminars / Mini Courses

  • IAS/PCMI Graduate Summer School: Motivic Homotopy

    • Combined Notes

      PDF, HTML

    • Danny Krashen, “Field arithmetic and the complexity of algebraic objects”

      PDF, HTML

    • Philippe Gille, “G-torsors over affine curves”

      PDF, HTML

    • Frédéric Déglise, “Motivic categories”

      PDF, HTML

    • Kirsten Wickelgren, “An introduction to $\AA^1$ homotopy theory using enumerative examples”

      PDF, HTML

    • Matthew Morrow, “Aspects of motivic cohomology”

      PDF, HTML

  • Reading Seminar: Salamon-McDuff, “J-Holomorphic Curves and Symplectic Topology”
  • VRG notes on tilings and translation surfaces:

    PDF, HTML

  • Arizona Winter School, 2019

    • Kirsten Wickelgren: A1 Enumerative Geometry

      PDF (Old version)

      PDF

    • Matthew Morrow: Topological Hochschild Homology in Arithmetic Geometry

      PDF

  • UCSD Algebraic Geometry Conference, 2019

    Talk Notes (PDF)

Expository

  • A note on motivating and using semidirect products to classifying finite groups: PDF

  • Classifying groups of order $pq$ using semidirect products: PDF

  • An expository paper on the history of modern Algebraic Geometry (2017): PDF

  • Some notes on the Math GRE:

    Notes, Slides (HTML), Slides (PDF).

  • 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!

Resources / Remarks on Live-Texing

Some tools I use:

Some useful resources:

Comments