PDF files

    • An older draft of my book “Incidence Theory” (with a focus on the polynomial method). For the published version, see here.
    • Polynomial method lecture notes (with a focus on incidences). These are mostly subsumed by the above book. The main exception is a proof of the complete 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
      • 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.
    • Additive combinatorics lecture notes:
    • The Konyagin-Shkredov sum-product bound – The proof of the sum-product bound of Konyagin and Shkredov, explained in detail.

Comments, questions, and complaints are welcome.

8 thoughts on “PDF files

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      • 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.

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