- The current draft of my book “Incidence Theory” (with a focus on the polynomial method). Additional chapters are gradually being added.
- Polynomial method lecture notes (with a focus on incidences). These are mostly subsumed by the above book. The only exception is a proof of the Guth-Katz distinct distances theorem that involves ruled surfaces and flat points.
- Chapter 1. Introduction to geometric incidences, related problems in discrete geometry, and first applications.
- Chapter 2. Some basic real algebraic geometry.
- Chapter 3. Polynomial partitioning and how to use it to obtain incidence bounds.
- Chapter 4. Constant-sized polynomial partitioning.
- Chapter 5. The joints problem.
- Chapter 6. The Elekes-Sharir-Guth-Katz
Framework. - Chapter 7. Lines in .
- Chapter 8. Distinct intersection points (finishing the Guth-Katz distinct distances problem).
- Chapter 9. More distinct distances problems.
- Additive combinatorics lecture notes:
- The Konyagin-Shkredov sum-product bound – The proof of the sum-product bound of Konyagin and Shkredov, explained in detail.
- Distinct Distances: Open Problems and Current Bounds – This is my ongoing attempt to survey the many open variants of the distinct distances problem, and the best known bounds for them. Occasionally I also include proofs, if they are short and elegant.
- The second-partitioning-polynomial technique.
Comments, questions, and complaints are welcome.
Advertisements
Pingback: The second-partitioning-polynomial technique (part 1) | Some Plane Truths
Pingback: Random Stories from IPAM – Part1 | Some Plane Truths
Pingback: Incidences in the complex plane | Some Plane Truths