Overview
My research interests lie in number theory and algebraic geometry. More specifically, I do a lot of work on non-Archimedean analytic spaces and their applications to algebraic and tropical geometry.
Current Appointments & Affiliations
Associate Professor of Mathematics
·
2019 - Present
Mathematics,
Trinity College of Arts & Sciences
Recent Publications
Total p-differentials on schemes over Z/p2
Journal Article Journal of Algebra · April 15, 2019 For a scheme X defined over the length 2 p-typical Witt vectors W2(k) of a characteristic p field, we introduce total p-differentials which interpolate between Frobenius-twisted differentials and Buium's p-differentials. They form a sheaf over t ... Full text CiteNon-Archimedean and tropical theta functions
Journal Article Mathematische Annalen · December 1, 2018 We define a tropicalization procedure for theta functions on abelian varieties over a non-Archimedean field. We show that the tropicalization of a non-Archimedean theta function is a tropical theta function, and that the tropicalization of a non-Archimedea ... Full text CiteDiophantine and tropical geometry, and uniformity of rational points on curves
Conference Proceedings of Symposia in Pure Mathematics · January 1, 2018 We describe recent work connecting combinatorics and tropical/ non-Archimedean geometry to Diophantine geometry, particularly the uniformity conjectures for rational points on curves and for torsion packets of curves. The method of Chabauty–Coleman lies at ... Full text CiteRecent Grants
RTG: Linked via L-functions: training versatile researchers across number theory
Inst. Training Prgm or CMEKey Faculty · Awarded by National Science Foundation · 2023 - 2028Development and Applications of Non-Archimedean Analytic Geometry and Tropical Geometry
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2019 - 2021View All Grants
Education, Training & Certifications
Stanford University ·
2009
Ph.D.