Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • 6 - Polynomial Methods in Finite Fields

  • Adam Sheffer, Bernard M. Baruch College, City University of New York
  • Book:
    Polynomial Methods and Incidence Theory
    Published online:
    17 March 2022
    Print publication:
    24 March 2022, pp 76-94

  • Summary

    In this chapter, we use polynomial methods to study incidence-related problems in spaces over finite fields. We focus on two breakthroughs: A solution to the finite field Kakeya problem and the cap set problem. The proofs of these results are short, elegant, and require mostly elementary tools. In Chapter 13, we study point-line incidences in spaces over finite fields, which require more involved arguments.

    This chapter contains a variety of other interesting problems and tools. We study the method of multiplicities, which improves the constant of the finite-field Kakeya theorem. To study the cap set problem, we use the slice rank technique. This technique is also used to obtain bounds for the 3-sunflower problem. As a warm-up towards the slice rank technique, we consider the Odd town problem and the two distance problem.