Graph Theory and Additive Combinatorics | Mathematics | MIT OpenCourseWare

Course Info

Instructor

Prof. Yufei Zhao

Departments

Mathematics

As Taught In

Fall 2019

Level

Graduate

Topics

Mathematics

Learning Resource Types

Instructor Insights

Lecture Notes

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Lecture Videos

Lecture 1: A bridge between graph theory and additive combinatorics

Lecture 2: Forbidding a Subgraph I: Mantel’s Theorem and Turán’s Theorem

Lecture 3: Forbidding a Subgraph II: Complete Bipartite Subgraph

Lecture 4: Forbidding a Subgraph III: Algebraic Constructions

Lecture 5: Forbidding a Subgraph IV: Dependent Random Choice

Lecture 6: Szemerédi’s Graph Regularity Lemma I: Statement and Proof

Lecture 7: Szemerédi’s Graph Regularity Lemma II: Triangle Removal Lemma

Lecture 8: Szemerédi’s Graph Regularity Lemma III: Further Applications

Lecture 9: Szemerédi’s Graph Regularity Lemma IV: Induced Removal Lemma

Lecture 10: Szemerédi’s Graph Regularity Lemma V: Hypergraph Removal and Spectral Proof

Lecture 11: Pseudorandom Graphs I: Quasirandomness

Lecture 12: Pseudorandom Graphs II: Second Eigenvalue

Lecture 13: Sparse Regularity and the Green-Tao Theorem

Lecture 14: Graph Limits I: Introduction

Lecture 15: Graph Limits II: Regularity and Counting

Lecture 16: Graph Limits III: Compactness and Applications

Lecture 17: Graph Limits IV: Inequalities between Subgraph Densities

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

Lecture 19: Roth’s Theorem II: Fourier Analytic Proof in the Integers

Lecture 20: Roth’s Theorem III: Polynomial Method and Arithmetic Regularity

Lecture 21: Structure of Set Addition I: Introduction to Freiman’s Theorem

Lecture 22: Structure of Set Addition II: Groups of Bounded Exponent and Modeling Lemma

Lecture 23: Structure of Set Addition III: Bogolyubov’s Lemma and the Geometry of Numbers

Lecture 24: Structure of Set Addition IV: Proof of Freiman’s Theorem

Lecture 25: Structure of Set Addition V: Additive Energy and Balog-Szemerédi-Gowers Theorem

Lecture 26: Sum-Product Problem and Incidence Geometry

Course Info

Instructor

Prof. Yufei Zhao

Departments

Mathematics

As Taught In

Fall 2019

Level

Graduate

Topics

Mathematics

Learning Resource Types

Instructor Insights

Lecture Notes

Lecture Videos

Problem Sets

Download Course

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