Pseudorandom graphs and the Green-Tao theorem | |
Student No.： | 40 |
Time： | Tue & Wed & Thu 17:05-18:40, Mar.27, 28, 29 |
Instructor： | Yufei Zhao |
Place： | Conference Room 3, Jin Chun Yuan West Bldg. |
Starting Date： | 2018-3-27 |
Ending Date： | 2018-3-29 |
Description: There has been a lot of exciting development in the past couple of decades in the area of additive combinatorics, which concerns the combinatorial structure of integers under simple operations such as addition. Its most spectacular result is the celebrated Green—Tao theorem, stating that the primes contain arbitrarily long arithmetic progressions. In this lecture series, I will highlight some connections between additive combinatorics and graph theory, and explain some of the key graph theoretic ideas in the proof of the Green-Tao theorem.
There will be three lectures on the subject. The lectures are related but may be enjoyed independently of each other.
(1) Overview of results in additive combinatorics, highlighting their connections to graph theory
(2) Szemerédi’s graph regularity method. Pseudorandom graphs
(3) Main ideas in the proof of the Green—Tao theorem
Prerequisite: None. No background in combinatorics and graph theory will be assumed.
Reference:
[1] MIT Math Graduate Course: Graph Theory and Additive Combinatorics, Fall 2017, http://yufeizhao.com/gtac/
[2] D. Conlon, J. Fox, and Y. Zhao, The Green-Tao theorem: an exposition, EMS Surv. Math. Sci. 1 (2014), 249–282. https://arxiv.org/abs/1403.2957