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 Duke Appointments & Affiliations
Associate Professor of Mathematics
·
2019 - Present
Mathematics,
Trinity College of Arts & Sciences
Recent Scholarly Works
FORMS ON BERKOVICH SPACES BASED ON HARMONIC TROPICALIZATIONS
Journal article Bulletin De La Societe Mathematique De France · January 1, 2026 We introduce tropical skeletons for Berkovich spaces based on results of Ducros. Then we study harmonic functions on good strictly analytic spaces over a non-trivially valued non-Archimedean field. Chambert-Loir and Ducros introduced bigraded sheaves of sm ... Full text CiteTotal 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 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 - 2029Development and Applications of Non-Archimedean Analytic Geometry and Tropical Geometry
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2019 - 2021View All Grants
Education
Stanford University ·
2009
Ph.D.