Overview
Professor Robles is a geometer. Her current research is focused on questions in complex geometry that are motivated by Hodge theory and its applications to moduli of algebraic varieties. (She also has made contributions to the fields of Finsler geometry, calibrated geometry, and complex projective geometry.) She also is also interested in (and supervises projects on) 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.