Expository writing

I have written survey papers, lecture notes for expository talks, not-for-publication expository notes, and lecture notes for classes at Canada/USA Mathcamp. These are all collected below.

Survey papers

Upper bounds on diagonal Ramsey numbers [after Campos, Griffiths, Morris, and Sahasrabudhe]

Lecture notes for expository talks

I have given many talks in student seminars, reading groups, etc., and have written lecture notes for a number of these talks.

Caveat lector! Many of these lecture notes are incomplete, full of typos, and completely bereft of references and citations.

Thresholds
Topological Methods in Combinatorics
My Favorite Theorem
Uniform Spanning Trees and Determinantal Point Processes
How Algebraic Geometers Could Prove P≠NP
Numbers and Graphs
The Entropy Method for Sidorenko's Conjecture
What's the Point?
Ramsey, randomness, and regularity,
Eudoxus, the most important mathematician you’ve never heard of
How (not) to poll
Claude Shannon, Master of Uncertainty
Turandotdotdot
Ramsey goodness (and beyond)
Multicolor Ramsey numbers
The singularity problem for discrete random matrices
Hypercontractivity
Applications of the subspace theorem
Ramsey multiplicity
Not your grandparents' linear algebra
Extremal numbers of subdivisions (and friends)
Dependent random choice

Expository notes

These are short expository notes which are not intended for publication.

Complete r-partite r-graphs are Sidorenko

The Erdős–Simonovits compactness conjecture needs more assumptions

An exposition of almost periodicity

Mathcamp classes

I have taught classes while a counselor at Canada/USA Mathcamp, a summer program for high-school students. Below are lecture notes and homework for most of these classes, some of which are week-long classes and some of which are shorter.

Caveat lector iterum! Many of these lecture notes are incomplete, full of typos, and completely bereft of references and citations. Additionally, some of these classes are very silly.

The Four Cube-Face Fun Fact of “The Barn” (aka Lagrange’s Four-Square Theorem, using words of length ≤ 4)
The Ham Sandwich Theorem and Friends
The Fast More Four Do Over (aka the Fast Fourier Transform, using words of length ≤ 4)
Harmonic Functions on Graphs
The Kakeya Conjecture
The Shannon Capacity of Graphs
Advanced Complex Analysis
The Kakeya Maximal Conjecture
The Combinatorial Nullstellensatz
The Szemerédi Regularity Lemma
Hedetniemi’s Conjecture
Ancient Greek Calculus
Crossing numbers
Euclidean geometry beyond Euclid
Martingales
Three-term arithmetic progressions
Extremal graph theory
The probabilistic method
Szemerédi’s {theorem, regularity lemma}
The uncertainty principle
Algebraic complexity
The law of anomalous numbers