Overview
I work on the geometry and arithmetic of figures defined by polynomial equations. I am especially interested in the geometry of algebraic curves, surfaces, threefolds and fourfolds over the complex numbers, over numbers fields, over finite fields, over fields of transcendence degree one over finite fields and over discrete valuation rings with perfect residue field. More specifically I study elliptic surfaces, elliptic threefolds, Calabi-Yau varieties, abelian varieties and surfaces of general type. I am interested in Chow groups of algebraic varieties and the relationship between a variety's Chow group and its arithmetic and geometric properties.
Current Appointments & Affiliations
Professor of Mathematics
·
1998 - Present
Mathematics,
Trinity College of Arts & Sciences
Recent Publications
HODGE NUMBERS OF DESINGULARIZED FIBER PRODUCTS OF ELLIPTIC SURFACES
Journal Article Proceedings of the American Mathematical Society · August 1, 2024 Each element of (Z≥0)2 is realized as the Hodge vector (h3,0(Z), h2,1(Z)) of some compact, connected, three dimensional, complex, submanifold, Z ⊂ PNC . Each (x, y) ∈ (Z≥1)2< ... Full text CiteA Non-Hyperelliptic Curve with Torsion Ceresa Cycle Modulo Algebraic Equivalence
Journal Article International Mathematics Research Notices · March 1, 2023 We exhibit a non-hyperelliptic curve C of genus 3 such that the class of the Ceresa cycle [C]-[C-] in JC modulo algebraic equivalence is torsion. ... Full text CiteOn certain complex projective manifolds with Hodge numbers H10 = 4 and h20 = 5
Journal Article Michigan Mathematical Journal · January 1, 2019 Full text CiteRecent Grants
Chow Groups of Projective Varieties
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2002 - 2006Chow Groups of Smooth Projective Varieties
ResearchPrincipal Investigator · Awarded by National Science Foundation · 1999 - 2003Mathematical Sciences: Chow Groups of Smooth Projective Varieties
ResearchPrincipal Investigator · Awarded by National Science Foundation · 1993 - 1996View All Grants
Education, Training & Certifications
The University of Chicago ·
1982
Ph.D.
Haverford College ·
1975
B.A.