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Course18.21726 lectures33 h 55 min

Graph Theory and Additive Combinatorics

Prof. Yufei Zhao · Massachusetts Institute of Technology

Start with lecture 1 At MIT OpenCourseWare

About

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.

Lectures

Video Lectures

  1. Lecture 1: A bridge between graph theory and additive combinatorics 1 h 17 min · Video
  2. Lecture 2: Forbidding a Subgraph I: Mantel’s Theorem and Turán’s Theorem 1 h 13 min · Video
  3. Lecture 3: Forbidding a Subgraph II: Complete Bipartite Subgraph 1 h 17 min · Video
  4. Lecture 4: Forbidding a Subgraph III: Algebraic Constructions 1 h 20 min · Video
  5. Lecture 5: Forbidding a Subgraph IV: Dependent Random Choice 1 h 20 min · Video
  6. Lecture 6: Szemerédi’s Graph Regularity Lemma I: Statement and Proof 1 h 20 min · Video
  7. Lecture 7: Szemerédi’s Graph Regularity Lemma II: Triangle Removal Lemma 1 h 15 min · Video
  8. Lecture 8: Szemerédi’s Graph Regularity Lemma III: Further Applications 1 h 22 min · Video
  9. Lecture 9: Szemerédi’s Graph Regularity Lemma IV: Induced Removal Lemma 1 h 24 min · Video
  10. Lecture 10: Szemerédi’s Graph Regularity Lemma V: Hypergraph Removal and Spectral Proof 1 h 20 min · Video
  11. Lecture 11: Pseudorandom Graphs I: Quasirandomness 1 h 19 min · Video
  12. Lecture 12: Pseudorandom Graphs II: Second Eigenvalue 1 h 20 min · Video
  13. Lecture 13: Sparse Regularity and the Green-Tao Theorem 1 h 20 min · Video
  14. Lecture 14: Graph Limits I: Introduction 1 h 18 min · Video
  15. Lecture 15: Graph Limits II: Regularity and Counting 1 h 22 min · Video
  16. Lecture 16: Graph Limits III: Compactness and Applications 1 h 20 min · Video
  17. Lecture 17: Graph Limits IV: Inequalities between Subgraph Densities 1 h 20 min · Video
  18. Lecture 18: Roth’s Theorem I: Fourier Analytic Proof over Finite Field 1 h 15 min · Video
  19. Lecture 19: Roth’s Theorem II: Fourier Analytic Proof in the Integers 1 h 21 min · Video
  20. Lecture 20: Roth’s Theorem III: Polynomial Method and Arithmetic Regularity 1 h 21 min · Video
  21. Lecture 21: Structure of Set Addition I: Introduction to Freiman’s Theorem 1 h 15 min · Video
  22. Lecture 22: Structure of Set Addition II: Groups of Bounded Exponent and Modeling Lemma 1 h 20 min · Video
  23. Lecture 23: Structure of Set Addition III: Bogolyubov’s Lemma and the Geometry of Numbers 1 h 19 min · Video
  24. Lecture 24: Structure of Set Addition IV: Proof of Freiman’s Theorem 1 h 20 min · Video
  25. Lecture 25: Structure of Set Addition V: Additive Energy and Balog-Szemerédi-Gowers Theorem 1 h 15 min · Video
  26. Lecture 26: Sum-Product Problem and Incidence Geometry 1 h 15 min · Video

Syllabus and materials

At MIT OpenCourseWare, as the course publishes them.

Credits and licence

Institution
Massachusetts Institute of Technology
Department
Mathematics
Teacher
Prof. Yufei Zhao
Term
Fall 2019
Level
Graduate
Language
English
Subjects
Mathematics
Source
MIT OpenCourseWare
Licence
CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only. MIT OpenCourseWare's terms
Attribution
Prof. Yufei Zhao. Graph Theory and Additive Combinatorics. Fall 2019. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
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