18.S997 Graph Theory and Additive Combinatorics

Fall 2017, MIT

Time: Tuesdays and Thursdays 9:30—11am

Class location: 2-139

Lecturer: Yufei Zhao

Course description

The course examines classical and modern developments in graph theory and additive combinatorics, with a focus on topics that connect the two subjects. Topics include: extremal graph theory, Szemerédi’s regularity lemma and applications, pseudorandom graphs, graph limits, Roth’s theorem and Szemerédi’s theorem on arithmetic progressions, Gowers uniformity norms, and the Green-Tao theorem. The course also introduces students to current research topics and open problems.

Here is a taste of some of the topics discussed in the course (time-permitting).

Although the course will be largely divided into two parts (graph theory in the first half and additive combinatorics in the second), we will emphasize the interactions between the two topics and highlight the common themes.

Prerequisite: Mathematical maturity at the level of a first-year math graduate student.

Grading

Lectures

Class participants will be responsible for writing and editing the course notes. More details coming soon.

Homework

There will be 3~4 graded homework assignments. Details to be decided.

In addition, there will be a continually updated list of ungraded exercises to provide practice with the course material.

References

The content of the course will primarily be drawn from several sources listed below.

Extremal graph theory

Pseudorandom graphs and graph limits

Additive combinatorics