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Last updated:

November 4, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

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.

Course Curriculum

  • A bridge Between graph theory and additive Combinatorics Unlimited
  • Forbidding a Subgraph 1: Mantel’s Theorem and Turan’s Theorem Unlimited
  • Forbidding a Subgraph 2: Complete Bipartite Subgraph Unlimited
  • Forbidding a Subgraph 3: Algebraic Constructions Unlimited
  • Forbidding a Subgraph 4: Dependent Randon Choice Unlimited
  • Szemeredi’s Graph Regularity Lemma 1: Statement and proof Unlimited
  • Szemeredi’s Graph Regularity Lemma 2: Triangle Removal Lemma Unlimited
  • Szemeredi’s Graph Regularity Lemma 3: Further Applications Unlimited
  • Szemeredi’s Graph Regularity Lemma 4: Induced Removal Lemma Unlimited
  • Szemeredi’s Graph Regularity Lemma 5: Hypergraph Removal nad Spectral Proof Unlimited
  • Pseudorandom Graph 1: Quasirandomness Unlimited
  • Pseudorandom Graph 2: Second Eigenvalue Unlimited
  • Sparse Regularity and the Green-Tao Theorem Unlimited
  • Graph Limits 1: Introduction Unlimited
  • Graph Limit 2: Regularity and Counting Unlimited
  • Graph Limit 3: Compactness and Applications Unlimited
  • Graph Limit 4: Inequalities Between Subgraph Densities Unlimited
  • Roth’s Theorem 1: Fourier Analytic Proof Over Finite Field Unlimited
  • Roth’s Theorem 2: Fourier Analytic Proof In the Integers Unlimited
  • Roth’s Theorem 3: Polynomial Method and Arithmetic Regularity Unlimited
  • Structure of Set Addition 1: Introduction to Freiman’s Theorem Unlimited
  • Structure of Set Addition 2: Groups of Bounded Exponent and Modeling Lemma Unlimited
  • Structure of Set Addition 3: Bogolyubov’s Lemma and the Geometry of Numbers Unlimited
  • Structure of Set Addition 4: Proof of Freiman’s Theorem Unlimited
  • Structure of Set Addition 5: Additive Energy and Balog-Szemeredi-Gowers Theorem Unlimited
  • Sum-Product Problem and Incidence Geometry Unlimited

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Massachusetts Institute of Technology