These are the notes of my last lecture in the 18.099 discrete analysis seminar. It is a very high-level overview of the Green-Tao theorem. It is a subset of this paper. 1. Synopsis This post as in overview of the proof of: Theorem 1 (Green-Tao) The prime numbers contain arbitrarily long arithmetic progressions. Here, Szemerédi's… Continue reading A Sketchy Overview of Green-Tao

# Tag: additive combinatorics

## Vinogradov’s Three-Prime Theorem (with Sammy Luo and Ryan Alweiss)

This was my final paper for 18.099, seminar in discrete analysis, jointly with Sammy Luo and Ryan Alweiss. We prove that every sufficiently large odd integer can be written as the sum of three primes, conditioned on a strong form of the prime number theorem. 1. Introduction In this paper, we prove the following result:… Continue reading Vinogradov’s Three-Prime Theorem (with Sammy Luo and Ryan Alweiss)

## 18.099 Transcript: Bourgain’s Theorem

As part of the 18.099 Discrete Analysis reading group at MIT, I presented section 4.7 of Tao-Vu's Additive Combinatorics textbook. Here were the notes I used for the second half of my presentation. 1. Synopsis We aim to prove the following result. Theorem 1 (Bourgain) Assume $latex {N \ge 2}&fg=000000$ is prime and $latex {A,… Continue reading 18.099 Transcript: Bourgain’s Theorem

## 18.099 Transcript: Chang’s Theorem

As part of the 18.099 discrete analysis reading group at MIT, I presented section 4.7 of Tao-Vu's Additive Combinatorics textbook. Here were the notes I used for the first part of my presentation. 1. Synopsis In the previous few lectures we've worked hard at developing the notion of characters, Bohr sets, spectrums. Today we put… Continue reading 18.099 Transcript: Chang’s Theorem