I L^{a}T_{e}Xed up lecture notes for many of the classes I have
taken; feel free to read through them or use them to review. If you find a mistake or typo, please let me know.

If you want to look over the `.tex` source for any of these notes, please send me an email.

Algebraic Geometry (Math 390C), taught by David Ben-Zvi in Spring 2016.

Algebraic Geometry (Math 392C), taught by Sam Raskin in Fall 2018.

Applications of QFT to Geometry (Math 392C), taught by Andy Neitzke in Fall 2017.

Bridgeland Stability (Math 392C), taught by Benjamin Schmidt in Spring 2019.

Differential Topology (Math 382D), taught by Lorenzo Sadun in Spring 2016.

Equivariant Homotopy Theory (Math 392C), taught by Andrew Blumberg in Spring 2017. See also: source on Github, version indexed by lecture.

Geometric Langlands (Math 390C), taught by David Ben-Zvi in Fall 2016.

**Geometric Langlands**(Math 390C), taught by David Ben-Zvi in Spring 2021.Index Theory (Math 392C) taught by Dan Freed in Spring 2018. (incomplete)

*K*-Theory (Math 392C), taught by Dan Freed in Fall 2015.Mathematical Gauge Theory (Math 393C), taught by Dan Freed in Spring 2019.

Mathematical Physics (Math 393C), taught by Thomas Chen in Fall 2017.

Mirror Symmetry (Math 392C), taught by Bernd Siebert in Fall 2019.

Measure Theory (Math 381C), taught by Luis Caffarelli in Fall 2015. (incomplete)

Methods of Applied Mathematics (Math 383C), taught by Todd Arbogast in Fall 2015.

Morse Theory (Math 392C) taught by Dan Freed in Fall 2018.

Quantum Complexity Theory (CS 395T), taught by Scott Aaronson in Fall 2016. (incomplete)

Quantum symmetries, notes from the MSRI intrductory workshop on quantum symmetries in January 2020.

Rational Homotopy Theory (Math 392C), taught by Jonathan Campbell in Fall 2015. (incomplete)

Representation Theory (Math 392C) taught by Sam Gunningham in Spring 2017.

Riemann Surfaces (Math 392C) taught by Tim Perutz in Spring 2016.

Riemannian Geometry (Math 392C) taught by Dan Freed in Spring 2017.

Seiberg-Witten Theory and Four-Manifold Topology (Math 392C) taught by Tim Perutz in Spring 2018.

Spin Geometry (Math 392C), taught by Eric Korman in Fall 2016.

Topological and geometric methods in QFT, from lectures at an NSF-CBMS conference on topological and geometric methods in QFT at Montana State University in summer 2017.

Topological phases of matter (Physics 392T), taught by Andrew Potter in Fall 2019.

Topological quantum field theory, taught by Katrin Wehrheim in Spring 2020 at UC Berkeley. (incomplete)

Algebraic geometry learning seminars:

Summer 2016 (website): on roughly the middle third of Ravi Vakil's algebraic geometry lecture notes

*The Rising Sea*.Fall 2016 (website): on the first several chapters of Milne's notes on algebraic groups. (incomplete)

Geometric Langlands Seminar, spring 2017: a continuation of David Ben-Zvi's fall 2016 class on the geometric Langlands program.

Geometric Satake Seminar, fall 2017: on the affine Grassmannian, perverse sheaves and their convolution, the Tannakian formalism, and the proof of the geometric Satake theorem.

Geometry and string theory seminars (website):

Spring 2018: on anomalies and higher symmetries in quantum field theory, with an aim towards understanding QCD

_{4}.Summer 2018: on higher symmetries and the appearance of gerbes, 2-groups, etc. in quantum field theory.

Fall 2018: on vertex algebras and their relationship to 4D quantum field theory.

Spring 2019, on the Costello-Gwilliam approach to free quantum field theories.

Gromov-Witten Theory Seminar, spring 2018 (website): on Gromov-Witten theory and quantum cohomology.

Homotopy theory learning seminars:

Summer 2016 (website): on three papers of Dwyer and Kan ([1] [2] [3]) that develop the hammock localization.

Fall 2016: on Jacob Lurie's proof of Waldhausen's main theorem (lecture notes).

Spring 2017: continuing to work through Jacob Lurie's proof of Waldhausen's main theorem (lecture notes).

Fall 2017: on Goodwillie calculus.

Fall 2018 (website): on families in the stable homotopy groups of the spheres.

Spring 2019: on Furuta's proof of the 10/8 theorem using equivariant homotopy theory.

**Fall 2020**: on Lurie's proof of the cobordism hypothesis. This is an online seminar organized as an incarnation of MIT's Juvitop seminar.PCMI Preparatory Seminar, summer 2019 (website): on various topics in topology, geometry, and physics that are the background to the PCMI 2019 Graduate Summer School lectures.

Quantum Topology and Categorification Seminar, spring 2017 (website): on Khovanov homology and Witten's derivation of the Jones polynomial from Chern-Simons theory.

A sequence of week-long courses in summer by and for graduate students, running each summer since 2017. See the website for more information.

Introduction to spectral sequences, taught by Adrian Clough and Richard Wong in summer 2017.

Spectral sequences in (equivariant) stable homotopy theory, taught by Adrian Clough and Richard Wong in summer 2017.

Hyperkähler geometry, taught by Omar Kidwai and Sebastian Schulz in summer 2017.

Characteristic classes, taught by me in summer 2017 and 2018.

Kähler geometry, taught by Max Stolarski in summer 2017. (incomplete)

Stacks, taught by Adrian Clough in summer 2018.

Topological field theory (notes in progress!), taught by me in summer 2019.

Differential Galois theory, taught by me and Rok Gregoric in summer 2019.

The comparison of two cohomology operations: Walkthrough of a simple calculation using bordism.

Fun with 𝓔(1)-modules and pin

^{c}bordism: A different way to compute bordism groups, this time using the Adams spectral sequence over 𝓔(1).2-local string bordism and the Adams spectral sequence: Using the Adams spectral sequence over 𝓐(2) to make some low-dimensional string bordism calculations.

Bordism and invertible field theories: an overview of the classification of invertible field theories using homotopy theory.

Topological phases and topological field theories: slides from a talk about my research. Talk given over Zoom at MSRI's grad student seminar, April 1, 2020.

Lattice models and TQFTs: slides from a talk about my research intended for a general audience (that includes you). Talk given at AT&T Foundry, Palo Alto, January 13, 2017.

An Introduction to Cohomology: Notes from a talk I gave to UT Austin's undergraduate math club on March 2, 2016.

The Card Game SET and Its Mathematics: A talk I gave to UT Austin's undergraduate math club on October 14, 2015.

X

_{Y}for Automata: A short guide on using the X_{Y}package to typeset automata in L^{a}T_{e}X.

In undergrad, I produced 2,424 PDF pages of L^{a}T_{e}X for my classes.
1,491 of those (61.5%) were lecture notes; the remainder was mostly homework or longer writing assignments. This
works out to just under three pages a day, seven days a week, during the academic quarter.

CS 109: Introduction to Probability for Computer Scientists, taught by Mehran Sahami in Spring 2013.

CS 109L: Statistical Programming with R, taught by Ben Holtz in Spring 2014.

CS 154: Automata and Complexity Theory, taught by Ryan Williams in Winter 2014.

CS 155: Computer and Network Security, taught by Dan Boneh and John Mitchell in Spring 2015.

CS 161: Analysis of Algorithms, taught by Serge Plotkin in Fall 2012.

CS 229: Machine Learning, taught by Andrew Ng in Fall 2013.

CS 240H: Functional Systems in Haskell, taught by David Mazières and Bryan O'Sullivan in Spring 2014.

CS 255: Introduction to Cryptography, taught by Dan Boneh in Winter 2013.

CS 355: Topics in Cryptography, taught by Dan Boneh in Spring 2014.

CS 468: Differential Geometry for Computer Science, taught by Adrian Butscher and Justin Solomon in Spring 2013.

CME 193: Introduction to Scientific Python, taught by Austin Benson and Dan Frank in January 2013.

History 154: The Early Intellectual History of America, taught by Justin duRivage in Winter 2015.

Math 53: Ordinary Differential Equations, taught by Akshay Venkatesh in Spring 2013.

Math 108: Combinatorics, taught by Kannan Soundararajan in Spring 2013.

Math 116: Complex Analysis, taught by Steve Kerckhoff in Fall 2014.

Math 120: Groups and Rings, taught by Søren Galatius in Fall 2012.

Math 121: Galois Theory, taught by Gregory Brumfiel in Winter 2013.

Math 122: Modules and Group Representations, taught by Gunnar Carlsson in Spring 2013.

Math 137: Mathematical Methods of Classical Mechanics, taught by Yakov Eliashberg in Winter 2013.

Math 144: Riemannian Geometry, taught by Rick Schoen in Winter 2014.

Math 145: Algebraic Geometry, taught by Ravi Vakil in Winter 2015.

Math 159: Discrete Probabilistic Methods, taught by Amir Dembo in Winter 2014.

Math 171: Fundamental Concepts of Analysis, taught by Rick Schoen in Spring 2014.

Math 205A: Measure Theory and Fourier Analysis, taught by Lenya Ryzhik in Fall 2014.

Math 210A: Modern Algebra I, taught by Zhiwei Yun in Fall 2013.

Math 210C: Lie Theory, taught by Akshay Venkatesh in Spring 2014.

Math 215B: Algebraic Topology, taught by Søren Galatius in Winter 2015.

Math 215C: Differential Topology, taught by Jeremy Miller in Spring 2015.

Math 217A: Differential Geometry, taught by Tian Yang in Fall 2014.

Math 217C: Complex Differential Geometry, taught by Eleny Ionel in Winter 2015. (incomplete)

Physics 40 series: Notes I took from the reading on Physics 41, 43, and 45.