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18.217 Graph Theory and Additive Combinatorics (Fall 2019, MIT OCW).
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Description
Instructor: Professor Yufei Zhao. 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. (from ocw.mit.edu)
Course content
- A Bridge between Graph Theory and Additive Combinatorics Unlimited
- Lecture 02 – Forbidding a Subgraph I: Mantel’s Theorem and Turan’s Theorem Unlimited
- Lecture 03 – Forbidding a Subgraph II: Complete Bipartite Subgraph Unlimited
- Lecture 04 – Forbidding a Subgraph III: Algebraic Constructions Unlimited
- Lecture 05 – Forbidding a Subgraph IV: Dependent Random Choice Unlimited
- Lecture 06 – Szemeredi’s Graph Regularity Lemma I: Statement and Proof Unlimited
- Lecture 07 – Szemeredi’s Graph Regularity Lemma II: Triangle Removal Lemma Unlimited
- Lecture 08 – Szemeredi’s Graph Regularity Lemma III: Further Applications Unlimited
- Lecture 09 – Szemeredi’s Graph Regularity Lemma IV: Induced Removal Lemma Unlimited
- Lecture 10 – Szemeredi’s Graph Regularity Lemma V: Hypergraph Removal and Spectral Proof Unlimited
- Lecture 11 – Pseudo-random Graph I: Quasirandomness Unlimited
- Lecture 12 – Pseudo-random Graph II: Second Eigenvalue Unlimited
- Lecture 13 – Sparse Regularity and the Green-Tao Theorem Unlimited
- Lecture 14 – Graph Limits I: Introduction Unlimited
- Lecture 15 – Graph Limits II: Regularity and Counting Unlimited
- Lecture 16 – Graph Limits III: Compactness and Applications Unlimited
- Lecture 17 – Graph Limits IV: Inequalities between Subgraph Densities Unlimited
- Lecture 18 – Roth’s Theorem I: Fourier Analytic Proof over Finite Field Unlimited
- Lecture 19 – Roth’s Theorem II: Fourier Analytic Proof in the Integers Unlimited
- Lecture 20 – Roth’s Theorem III: Polynomial Method and Arithmetic Regularity Unlimited
- Lecture 21 – Structure of Set Addition I: Introduction to Freiman’s Theorem Unlimited
- Lecture 22 – Structure of Set Addition II: Groups of Bounded Exponent and Modeling Lemma Unlimited
- Lecture 23 – Structure of Set Addition III: Bogolyubov’s Lemma and the Geometry of Numbers Unlimited
- Lecture 24 – Structure of Set Addition IV: Proof of Freiman’s Theorem Unlimited
- Lecture 25 – Structure of Set Addition V: Additive Energy and Balog-Szemeredi-Gowers Theorem Unlimited
- Lecture 26 – Sum Product Problem and Incidence Geometry Unlimited
Instructor
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