Christopher Keyes
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Research Interests

I am interested in arithmetic statistics, the study of the distribution of arithmetic objects including primes, number fields, points on curves, and families of curves.

Publications and Preprints

  1. On the density of locally soluble superelliptic curves (joint with Lea Beneish). Submitted. (arxiv, slides)
  2. Fields generated by points on superelliptic curves (joint with Lea Beneish). Submitted. (arxiv)
  3. Mertens' theorem for Chebotarev sets (joint with Santiago Arango-Piñeros and Daniel Keliher). Accepted for publication in International Journal of Number Theory. (arxiv)
  4. Growth of points on hyperelliptic curves. Accepted for publication in Journal de Théorie des Nombres de Bordeaux. (arxiv)
  5. Bounding the number of arithmetical structures on graphs (joint with Tomer Reiter). Discrete Mathematics, Volume 344, Issue 9, 2021. (journal, arxiv, slides, video)

Invited Talks

  1. Local solubility in families of superelliptic curves. Algebra, Geometry, and Number Theory Seminar, University of South Carolina, April 8, 2022.
  2. On the proportion of everywhere locally soluble superelliptic curves. (Secret) Algebra, Geometry, and Number Theory Seminar, Tufts University, November 18, 2021. (slides)
  3. Chip-firing games and arithmetical structures on graphs. WashU Undergraduate Mathematics Seminar, Washington University in St. Louis (held virtually), November 9, 2021.
  4. Fields generated by points on superelliptic curves (joint talk with Lea Beneish). UW Number Theory Seminar, University of Washington (held virtually), June 8, 2021.
  5. Counting number fields: problems and progress. WashU Undergraduate Mathematics Seminar, Washington University in St. Louis (held virtually), January 29, 2021.

Contributed Talks

  1. On the proportion of everywhere locally soluble superelliptic curves. Upstate Number Theory Conference, Union College, October 23, 2021.
  2. Fields generated by points on superelliptic curves. Young Researchers in Number Theory (Y-RANT), University of Bristol (held virtually), August 20, 2021.
  3. Mertens' product theorem for primes in Chebotarev sets. Front Range Number Theory Day (held virtually), April 24, 2021.
  4. An upper bound for the number of arithmetical structures on a graph. Mid-Atlantic Seminar on Numbers (MASON) V (held virtually), March 27, 2021.
  5. An upper bound for the number of arithmetical structures on a graph. PAlmetto Joint Arithmetic, Modularity, and Analysis Series (PAJAMAS), University of South Carolina (held virtually), December 6, 2020. (slides)
  6. Growth of points on hyperelliptic curves. Tufts Undergraduate Research Symposium, Tufts University, May 3, 2018.
  7. Growth of points on hyperelliptic curves. PAlmetto Number Theory Series (PANTS) XXVIII, University of Tennessee Knoxville, September 17, 2017.