Research Interests

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

Lately, my research has centered on questions of the form how often does an equation of a given shape have (certain kinds of) solutions? Some "shapes" of equations I find myself think about include hyperelliptic and superelliptic curves, hypersurfaces in projective space, and stacky curves arising from generalized Fermat equations. The solutions of interest are typically rational or integral points, but higher degree points and local (i.e. p-adic) solutions are also interesting.

You can read my research statement here.

Publications and Preprints

Preprints

Publications

Thesis

My PhD thesis, titled Topics in arithmetic statistics, is available online. It essentially consists of papers 2 - 5 above, together with a unifying introduction and some preliminary material.

Invited Talks

Contributed Talks

6. (slides)

Travel, past and future

Jan 2026	Joint Math Meetings, Washington, D.C., USA
Oct/Nov 2025	Focused Research Group, BIRS, Banff, Canada
September 2025	Geometric and Analytic Number Theory, University of Bath, UK
June/July 2025	Research in Groups, ICMS, Edinburgh, UK
June 2025	Research in Residence, CIRM, Luminy, France
January 2025	Joint Math Meetings, Seattle, WA, USA
December 2024	Research in Teams, BIRS, Banff, Canada
June 2024	Research in Groups, ICMS, Edinburgh, UK
April 2024	Utrecht Geometry Seminar, Utrecht, Netherlands
June 2023	MRC on Stacks, Java Center, NY, USA
May 2023	INTEGERS Conference, Athens, GA, USA
March 2023	Arizona Winter School, Tucson, AZ, USA
February 2023	MSRI Introductory Workshop on Diophantine Geometry, Berkeley, CA, USA
January 2023	Joint Math Meetings, Boston, MA, USA