Learn · Graph Theory and Additive Combinatorics

Lecture 18 of 26Lecture Videos1 h 15 min

Lecture 18: Roth’s Theorem I: Fourier Analytic Proof over Finite Field

Prof. Yufei Zhao · Massachusetts Institute of Technology

At MIT OpenCourseWare Transcript

Credits and licence

From
Graph Theory and Additive Combinatorics, Massachusetts Institute of Technology (at MIT OpenCourseWare)
Licence
CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only.
Attribution
Prof. Yufei Zhao. Graph Theory and Additive Combinatorics. Fall 2023. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
Who can watch
Tweens profiles and older. How courses are placed

All the 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