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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.
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English
English [CC]
FREE
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- Learn what is a programming language and the basic concepts for beginners.
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Description
The course also introduces students to current research topics and open problems.
Course content
- 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
Instructor
Massachusetts Institute of Technology
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