# PDF files

• 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 ${\mathbb R}^3$.
• Chapter 8. Distinct intersection points (finishing the Guth-Katz distinct distances problem).
• Chapter 9. More distinct distances problems.

• 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.

## 8 thoughts on “PDF files”

1. asahay22 |

This is a minor quibble, but should Theorem 6.5 say C(d,2) + 2d + 2, and not C(d,2) + 3d + 2?

• asahay22 |

In the Incidence Theory book, that is.

• Adam Sheffer |

Dear Anurag,

In the terms of the form $x_k x_\ell$, we also include that case of $k=\ell$. This means that there are $\binom{d}{2}+d$ such terms. So this is not a mistake, but it might indeed be nice to add a clarification there.

If you find any other issues, I’m always happy to hear about them. It’s better to email me than to write about it here.

• asahay22 |

Ahh fair, thanks for the clarification! I do have some more comments/questions on that section, I’ll write you a mail when I get some time.