---
res:
  bibo_abstract:
  - In 1873, James C. Maxwell conjectured that the electric field generated by n point
    charges in generic position has at most (n-1)^2 isolated zeroes. The first (nonoptimal)
    upper bound was only obtained in 2007 by Gabrielov, Novikov, and Shapiro, who
    also posed two additional interesting conjectures. In this article, we give the
    best upper bound known to date on the number of zeroes of the electric field,
    and construct a counterexample to Conjecture 1.8 by Gabrielov, Novikov, and Shapiro
    that the number of equilibria cannot exceed those of the distance function defined
    by the unit point charges. Finally, we note that it is quite possible that Maxwell's
    quadratic upper bound is not tight, so it is prudent to find lower bounds. Hence,
    we also explore examples and construct configurations of charges achieving the
    highest ratios of the number of electric field zeroes by point charges found to
    this day.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Herbert
      foaf_name: Edelsbrunner, Herbert
      foaf_surname: Edelsbrunner
      foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-9823-6833
  - foaf_Person:
      foaf_givenName: Christopher D
      foaf_name: Fillmore, Christopher D
      foaf_surname: Fillmore
      foaf_workInfoHomepage: http://www.librecat.org/personId=35638A5C-AAC7-11E9-B0BF-5503E6697425
  - foaf_Person:
      foaf_givenName: Goncalo
      foaf_name: Oliveira, Goncalo
      foaf_surname: Oliveira
      foaf_workInfoHomepage: http://www.librecat.org/personId=58abbde8-f455-11eb-a497-98c8fd71b905
  bibo_doi: 10.1112/plms.70163
  bibo_issue: '5'
  bibo_volume: 132
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0024-6115
  - http://id.crossref.org/issn/1460-244X
  dct_language: eng
  dct_publisher: Wiley@
  dct_title: Counting equilibria of the electrostatic potential@
...