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

Algebra

Abstract Algebra

Dan Nakano, Fall 2019

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Commutative Algebra

Pete Clark, Spring 2020

PDF

Daniel Litt, Spring 2022

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Homological Algebra

Brian Boe, Spring 2021

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Representation Theory

Lie Algebras

Chun-Ju Lai, Fall 2019

PDF

Brian Boe, Fall 2022

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Category $\OO$

Brian Boe, Spring 2020

PDF V2, HTML V2

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Algebraic Groups

Dan Nakano, Fall 2020

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Cohomology in Representation Theory

Dan Nakano, Spring 2022

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Categorification

Arik Wilbert, Summer 2020

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Flag Varieties, Equivariant Cohomology, and K Theory

Scott Larson, Fall 2021

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Algebraic Geometry

Varieties

Philip Engel, Fall 2020

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Schemes

Phil Engel, Fall 2021

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Sheaf Cohomology

Valery Alexeev, Spring 2022

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4-Manifolds and Algebraic Surfaces

Phil Engel, Spring 2021

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Moduli: GIT

Valery Alexeev, Fall 2022

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Moduli: Deformations

Ben Bakker, Spring 2020

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Arithmetic Geometry and Number Theory

Algebraic Number Theory

Paul Pollack, Spring 2021

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Galois Cohomology and Class Field Theory

Pete Clark, Spring 2021

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Algebraic Curves

Pete Clark, Fall 2020

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Étale Cohomology

Daniel Litt, Fall 2020

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Rational Points

Daniel Litt, Fall 2021

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Topology

Algebraic Topology

Justin Roberts, Fall 2017 and Spring 2018

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Morse Theory

Akram Alishahi, Spring 2020

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Floer Homology

Akram Alishahi, Spring 2021

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Characteristic Classes

Akram Alishahi, Fall 2021

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Contact Topology

Peter Lambert Colne, Spring 2022

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Analysis

Real Analysis

Neil Lyall, Fall 2019

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Complex Analysis

Jingzhi Tie, Spring 2020

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Undergrad

Undergraduate Compendium

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

(Self study, Spring 2017)

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Combinatorics

A study guide for undergraduate Combinatorics.

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Smooth Manifolds

Notes on Lee’s smooth manifolds.

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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

  • 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:

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