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
Period 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 CitePseudoconvexity at infinity in Hodge theory: a codimension one example
Journal article · February 9, 2023 The generalization of the Satake--Baily--Borel compactification to arbitrary period maps has been reduced to a certain extension problem on certain "neighborhoods at infinity". Extension problems of this type require that the neighborhood be pseudoconvex. ... 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 - 2028Complex Geometric Properties of Period Maps
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2023 - 2027Complex Geometric and Lie Theoretic Aspects of Hodge Theory
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2019 - 2023View All Grants
Education
University of British Columbia (Canada) ·
2003
Ph.D.