Graph Theory and Additive Combinatorics
Introduction to extremal graph theory and additive combinatorics. Highlights common themes, such as the dichotomy between structure versus pseudorandomness. Topics include Turan-type problems, Szemeredi's regularity lemma and applications, pseudorandom graphs, spectral graph theory, graph limits, arithmetic progressions (Roth, Szemeredi, Green-Tao), discrete Fourier analysis, Freiman's theorem on sumsets and structure. Discusses current research topics and open problems.
Fall 2023
This course examines classical and modern developments in graph theory and additive combinatorics, with a focus on topics and themes that connect the two subjects. The course also introduces students to current research topics and open problems. This course was previously numbered 18.217.
Readings
- Zhao, Yufei. Graph Theory and Additive Combinatorics: Exploring Structure and Randomness . Cambridge University Press, 2023. ISBN: 9781009310949.
Prerequisites & course information
Prereq: (( 18.701 or 18.703 ) and ( 18.100A , 18.100B , 18.100P , or 18.100Q )) or permission of instructor Acad Year 2027-2028: Not offered Acad Year 2028-2029: G (Spring) 3-0-9 units
Sources
- Course catalogue ↗2026–2027
- MIT OpenCourseWare ↗Fall 2023
- MIT OCW calendar ↗
- MIT OCW syllabus ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.