Current Appointments & Affiliations
Professor of Mathematics
·
2020 - Present
Mathematics,
Trinity College of Arts & Sciences
Recent Publications
GENERALISED QUADRATIC FORMS OVER TOTALLY REAL NUMBER FIELDS
Journal Article Journal of the Institute of Mathematics of Jussieu · November 1, 2024 We introduce a new class of generalised quadratic forms over totally real number fields, which is rich enough to capture the arithmetic of arbitrary systems of quadrics over the rational numbers. We explore this connection through a version of the Hardy-Li ... Full text CiteOn Polynomial Carleson Operators Along Quadratic Hypersurfaces
Journal Article Journal of Geometric Analysis · October 1, 2024 We prove that a maximally modulated singular oscillatory integral operator along a hypersurface defined by (y,Q(y))⊆Rn+1, for an arbitrary non-degenerate quadratic form Q, admits an a priori bound on Lp for all 1 Full text CiteA NEW TYPE OF SUPERORTHOGONALITY
Journal Article Proceedings of the American Mathematical Society · February 1, 2024 We provide a simple criterion on a family of functions that implies a square function estimate on Lp for every even integer p ≥ 2. This defines a new type of superorthogonality that is verified by checking a less restrictive criterion than any other type o ... Full text CiteRecent Grants
RTG: Linked via L-functions: training versatile researchers across number theory
Inst. Training Prgm or CMECo-Principal Investigator · Awarded by National Science Foundation · 2023 - 2028Class Groups, Character Sums, and Oscillatory Integrals
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2022 - 2025Investigations in the intersection of number theory and harmonic analysis
ResearchPrincipal Investigator · Awarded by Simons Foundation · 2024 - 2024View All Grants