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Higher Distance Energies and Expanders with Structure

Pohoata, Cosmin and Sheffer, Adam (2017) Higher Distance Energies and Expanders with Structure. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20200110-160143789

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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.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1709.06696arXivDiscussion Paper
ORCID:
AuthorORCID
Sheffer, Adam0000-0003-3418-5122
Additional Information:Supported by NSF grant DMS-1710305.
Funders:
Funding AgencyGrant Number
NSFDMS-1710305
Record Number:CaltechAUTHORS:20200110-160143789
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200110-160143789
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100649
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 Jan 2020 00:51
Last Modified:11 Jan 2020 00:51

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