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 Appointments & Affiliations
Professor of Mathematics
·
2020 - Present
Mathematics,
Trinity College of Arts & Sciences
Assistant Director of the Rhodes Information Initiative at Duke
·
2024 - Present
Rhodes Information Initiative at Duke,
University Initiatives & Academic Support Units
Recent Publications
Completion of two-parameter period maps by nilpotent orbits
Preprint · December 1, 2023 We show that every two-parameter period map admits a Kato--Nakayama--Usui completion to a morphism of log manifolds. ... Open Access Link to item CitePseudoconvexity at infinity in Hodge theory: a codimension one example
Preprint · 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 CiteExtension of Hodge norms at infinity
Preprint · February 8, 2023 It is a long-standing problem in Hodge theory to generalize the Satake--Baily--Borel (SBB) compactification of a locally Hermitian symmetric space to arbitrary period maps. A proper topological SBB-type completion has been constructed, and the problem of s ... 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 - 2026Complex Geometric and Lie Theoretic Aspects of Hodge Theory
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2019 - 2023View All Grants
Education, Training & Certifications
University of British Columbia (Canada) ·
2003
Ph.D.