https://orcid.org/0000-0002-5908-9551
Overview
I am a geometer. My current research addresses the complex geometry of period maps, and related questions that are Hodge theory and its applications to moduli of algebraic varieties. I have also made contributions to the fields of Finsler geometry, calibrated geometry, and complex projective geometry. I have a side interest in the formalization of mathematics via automated theorem-provers and proof-assistants (such as Lean).
Current Duke Appointments & Affiliations
Professor of Mathematics
·
2020 - Present
Mathematics,
Trinity College of Arts & Sciences
Recent Scholarly Works
Analog of Satake–Baily–Borel for period maps
Journal article European Journal of Mathematics · September 1, 2026 We propose an analog of the Satake–Baily–Borel compactification and Borel’s extension theorem for arbitrary period maps. The proposed analog is constructed as a proper topological completion of the period map. It is conjectured that the construction is pro ... Full text CitePeriod maps at infinity
Preprint · September 10, 2025 Link to item CiteCompletion of two-parameter period maps by nilpotent orbits
Journal article · December 1, 2023 We show that every two-parameter period map admits a Kato--Nakayama--Usui completion to a morphism of log manifolds, and the map onto the image is a morphism of compact algebraic spaces. This result also applies to the case of mixed period maps and we use ... Open Access Link to item 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 - 2029Complex geometry and differential invariants of period maps
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2026 - 2028Complex Geometric Properties of Period Maps
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2023 - 2027View All Grants
Education
University of British Columbia (Canada) ·
2003
Ph.D.