Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published January 11, 2020 | Submitted
Report Open

Higher Distance Energies and Expanders with Structure

Abstract

We adapt the idea of higher moment energies, originally used in Additive Combinatorics, so that it would apply to problems in Discrete Geometry. This new approach leads to a variety of new results, such as (i) Improved bounds for the problem of distinct distances with local properties. (ii) Improved bounds for problems involving expanding polynomials in R[x,y] (Elekes-Ronyai type bounds) when one or two of the sets have structure. Higher moment energies seem to be related to additional problems in Discrete Geometry, to lead to new elegant theory, and to raise new questions.

Additional Information

Supported by NSF grant DMS-1710305.

Attached Files

Submitted - 1709.06696.pdf

Files

1709.06696.pdf
Files (291.2 kB)
Name Size Download all
md5:7919ec10ccf1dc58a2550ed2ac16a567
291.2 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 18, 2023