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
Stanford’s Combinatorics Reading Seminar. May 26, 2017 [lecture notes]
- 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
Stanford’s Combinatorics Reading Seminar. October 19, 2018 [lecture notes]
- 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)
Stanford–MIT combinatorics reading seminar. June 9, 2020 [lecture notes]
- Multicolor Ramsey numbers
Stanford–MIT combinatorics reading seminar. October 6, 2020 [lecture notes]
- The singularity problem for discrete random matrices
- Hypercontractivity
- Applications of the subspace theorem
Stanford–MIT combinatorics reading seminar. July 1 and 8, 2021 [lecture notes]
- Ramsey multiplicity
Stanford’s Combinatorics Reading Seminar. October 4, 2021 [lecture notes]
- Not your grandparents' linear algebra
- Extremal numbers of subdivisions (and friends)
Stanford’s Combinatorics Reading Seminar. April 22, 2022 [lecture notes]
- Dependent random choice
Tel Aviv University Combinatorics Reading Seminar. March 21, 2023 [lecture notes]
Mathcamp classes
I have taught classes while a counselor at Canada/USA Mathcamp, and I made lecture notes and homework for most of them.
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
- Math and Literature
- The Kakeya Conjecture
- The Shannon Capacity of Graphs
- Ancient Greek Mathematics
- Advanced Complex Analysis
- The Kakeya Maximal Conjecture
- The Combinatorial Nullstellensatz
- The Szemerédi Regularity Lemma
- Fast Matrix Multiplication
- Hedetniemi’s Conjecture
- Ancient Greek Calculus
- Crossing numbers
- Euclidean geometry beyond Euclid
- Martingales
- Three-term arithmetic progressions
Colloquium at Mathcamp 2022 [slides]
- Extremal graph theory
- The probabilistic method
- Szemerédi’s {theorem, regularity lemma}
- Ancient Greek mathematics
- The uncertainty principle
- The Combinatorial Nullstellensatz
- Why June Huh won the Fields Medal