Notes
I like to LaTeX notes; some of these notes are posted here. For all of these notes, all content is due to the professor (for lecture notes) or speaker (for talk notes), while all errors are due to me.
Lecture notes
Here are notes from some subset of the classes I’ve taken at MIT.
For fun, I occasionally return to old notes to clean them up and add diagrams. Notes listed in gray are ones for which I haven’t yet done so. These aren’t at the level of polish I’d like, and may get updated in the future.
- 6.1220: Design and Analysis of Algorithms, Fall 2022 [notes] Taught by Piotr Indyk, Srini Raghuraman, and Bruce Tidor.
- 6.5350: Matrix Multiplication and Graph Algorithms, Spring 2025 [notes] Taught by Virginia Vassilevska Williams.The 3/6 lecture is currently missing.
- 18.100B: Real Analysis, Fall 2022 [notes] Taught by Tobias Colding.
- 18.102: Introduction to Functional Analysis, Spring 2024 [notes] Taught by Marjorie Drake.
- 18.112: Functions of a Complex Variable, Fall 2023 [notes] Taught by Andrew Lawrie.A few lectures (9/28, 11/7, 11/9, and 11/14) are currently missing.
- 18.212: Algebraic Combinatorics, Spring 2022 [notes] Taught by Alex Postnikov.
- 18.217: Young Tableaux, Fall 2022 [notes] Taught by Alex Postnikov.A polished version of the first 23 pages (with better diagrams) can be found here.
- 18.218: Ramsey Theory, Spring 2023 [notes] Taught by Lisa Sauermann.
- 18.218: Analysis of Boolean Functions, Spring 2024 [notes] Taught by Dor Minzer.
- 18.225: Graph Theory and Additive Combinatorics, Fall 2023 [notes] Taught by Yufei Zhao.
- 18.226: Probabilistic Methods in Combinatorics, Fall 2022 [notes] Taught by Yufei Zhao.Most of the 9/19 lecture is currently missing.
- 18.404: Intro to the Theory of Computation, Fall 2023 [notes] Taught by Michael Sipser.
- 18.405: Advanced Complexity Theory, Spring 2024 [notes] Taught by Ryan Williams.
- 18.415: Advanced Algorithms, Fall 2024 [notes] Taught by David Karger.
- 18.615: Introduction to Stochastic Processes, Spring 2025 [notes] Taught by Elchanan Mossel.
- 18.619: Discrete Probability and Stochastic Processes, Spring 2025 [notes] Taught by Kuikui Liu.
- 18.675: Theory of Probability, Fall 2024 [notes] Taught by Konstantinos Kavvadias.The first 20 minutes of the first lecture are currently missing.
- 18.676: Stochastic Calculus, Spring 2025 [notes] Taught by Sky Cao.
- 18.701: Algebra I, Fall 2021 [notes] Taught by Davesh Maulik.
- 18.702: Algebra II, Spring 2022 [notes] Taught by Roman Bezrukavnikov.
- 18.901: Intro to Topology, Spring 2023 [notes] Taught by Anthony Conway.As of now, these notes only cover the first half of the class. (The second half may be added later.)
I’ve also contributed to the MIT OCW student notes for 18.701 and 18.702.
Reading group seminar
Here are my notes from some of the talks at a reading group seminar at MIT.
- Furstenberg–Sárközy [notes] Based on a paper of Green and Sawhney (link).
- Few distinct distances with forbidden 4-point patterns [notes] Based on a paper by Tao (link).
- Hamilton transversals in tournaments [notes] Based on a paper of Chakraborti, Kim, Lee, and Seo (link).
- Sum-product growth [notes] Based on a paper of Bourgain and Chang (link).
- Andrews's theorem [notes] Based on notes by Travis and papers of Konyagin and Sevast'yanov (link) and Kannan and Lovász (link).
- Partial coloring from volume lower bounds [notes]
- Thresholds, sharp thresholds, 2nd moment methods, and planted models [notes]
- Sharp thresholds in inference of planted subgraphs [notes] Based on a paper of Mossel, Niles-Weed, Sohn, Sun, and Zadik (link).
- Grothendieck problems on graphs [notes]
- A tutorial on the spread method [notes]
- An exponential improvement for Ramsey numbers [notes] Continuation of the previous day's colloquium talk.
- The corners problem over finite fields [notes]
- VC-dimension, regularity, and the Erdős–Hajnal conjecture [notes] Based on a paper by Fox, Pach, and Suk (link).
- Explicit separations between deterministic and randomized NOF communication [notes] Based on a paper by Kelley, Lovett, and Meka (link).
- The sum-difference conjecture [notes] Based on a paper by Katz and Tao (link).
- The periodic tiling conjecture [notes]
- Phase transitions in Bernoulli percolation [notes] Based on a paper by Duminil-Copin and Tassion (link).
- Polynomial Szemerédi in finite fields [notes] Based on a paper by Peluse (link).
- Same type lemma [notes] Based on a paper by Bukh and Vasileuski (link).
- Asymptotics of $r(4, t)$ [notes] Based on a paper by Mattheus and Verstraete (link).
- Hypergraph Ramsey [notes]
- Topological methods in combinatorics [notes]
- The density of unit-distance avoiding sets [notes] Based on papers by Ambrus, Csizárik, Matolcsi, Varga, and Zsámboki (link), Keleti, Matolcsi, Oliveira, and Ruzsa (link), and Ambrus and Matolcsi (link).
- Flat Littlewood polynomials exist [notes] Based on a paper by Balister, Bollobás, Morris, Sahasrabudhe, and Tiba (link).
- The hypergraph Moore bound [notes] Based on a paper by Hsieh, Kothari, and Mohanty (link).
- Lognormal limit for the symmetric perceptron [notes] Based on a paper by Abbe, Li, and Sly (link). It is likely that some things discussed in the talk are missing.
- Asymptotic enumeration for matroids [notes] Based on a paper by Bansal, Pendavingh, and van der Pol (link).
- Combinatorial interpretations [notes] Here is a link to Igor Pak's survey on this topic.
- Szemerédi's theorem and inverse theory of the Gowers norms [notes]
- Sum-free subsets of integers [notes]
- Ergodic theory in combinatorics [notes]
Other talks
Here are my notes from a few other talks I’ve attended; most are from the Richard P. Stanley Seminar in Combinatorics, and a few are from colloquium talks at MIT. (Note that these have many errors or holes.)
- Ordering by vantage points and sign patterns [notes] At the MIT Combinatorics Seminar.
- Quasipolynomial bounds for the corners theorem [notes] At the MIT Combinatorics Seminar.
- Non-existence probabilities and lower tails via Gibbs uniqueness on hypertrees [notes] At the MIT Combinatorics Seminar.
- Simulating time with square-root space [notes] At the MIT Theory of Computing Colloquium.
- Bounds for 3-progressions [notes] At the MIT Combinatorics Seminar.
- Locally sampleable uniform symmetric distributions [notes] At the MIT Algorithms and Complexity Seminar.
- Cutsets and percolation [notes] At the MIT Probability Seminar.
- Positive codegree thresholds in 3-graphs [notes] At JMM 2025.
- Dependent random choice, statistical physics, and local rank [notes] At the MIT Combinatorics Seminar.
- Additive combinatorics without addition — Ramsey Cayley graphs, information theory, and independence in random graph models [notes] At the MIT Combinatorics Seminar.
- Seeded embeddings and Ramsey numbers of bipartite graphs of sublinear bandwidth [notes] At the MIT Combinatorics Seminar.
- Uncommon systems of linear equations [notes] At the MIT Combinatorics Seminar.
- Lower bounds for incidences [notes] At the MIT Combinatorics Seminar.
- A new lower bound for sphere packing [notes] At the MIT Combinatorics Seminar.
- Diagonal Ramsey numbers and high dimensional geometry [notes] At the MIT Math Colloquium. The proof was discussed in more detail in the following day's reading group.
- Random reconstruction in two dimensions [notes] At the MIT Combinatorics Seminar.
- Heilbronn's triangle problem and projection theory [notes] At the MIT Combinatorics Seminar.
- Pair constructions for hypergraph Ramsey numbers [notes] At the MIT Combinatorics Seminar.
- Antichain codes [notes] At the MIT Combinatorics Seminar.
- Edge-statistics in Ramsey graphs [notes] At the MIT Combinatorics Seminar.
- Thresholds for Latin squares and Steiner triple systems [notes] At the MIT Combinatorics Seminar.
- Towards the Erdős–Gallai cycle decomposition conjecture [notes] At the MIT Combinatorics Seminar.
- A proof of the Kahn—Kalai conjecture [notes] At the MIT Combinatorics Seminar. Continuation of the previous day's colloquium talk.
- Thresholds [notes] At the MIT Math Colloquium. The proof was discussed in more detail in the following day's combinatorics seminar.