Research and Publications:
I earned my PhD in mathematics from the University of Arizona in 2007, and my mathematics research is in arithmetic geometry. This is a beautiful and challenging field in which techniques of algebraic geometry are applied to questions in number theory. In current work I study abelian varieties over function fields and finite fields. My undergraduate work was in mathematics education, and I am a (temporarily?) retired middle school and high school mathematics teacher. Since my own high school years, I have been concerned about academics and equity issues in our public schools. As the director of mathematics teacher education at Stony Brook, I now enjoy working with some of our nation's best current and future teachers.
Department of Mathematics
Professional Education Program
My Erdös number is 3.
Recent and Upcoming Conferences and Presentations:
- Attending to Precision: Mathematical Definitions in Courses for Pre-service and Practicing Teachers. To appear in PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies.
- Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields. (with C. Hall, R. Pannekoek, J Park, R. Pries, S. Sharif, A. Silverberg, and D. Ulmer) To appear in Memiors of the American Mathematical Society.
- Mathematical Language and the Common Core Standards for English. English Journal 102.5 (2013) 16-20.
- Equivalence Relations Across the Secondary Curriculum. Mathematics Teacher 106 (2013) 508-512.
- Elliptic curves with bounded ranks in function field towers. Acta Arithmetica 156 (2012), 301-323.
- Universal number partition problem with divisibility. (with M. Dror and J. Lynch) Discrete Mathematics 312 (2012) 1692-1698.
- The l-rank structure of a global function field. (with J.-L. Hoelscher, Y. Lee, J. Paulhus and R. Scheidler). Fields Institute Communications Series 60 American Mathematical Society, Providence, RI, (2011), 145-166.
- Towers of surfaces dominated by products of curves and elliptic curves of large rank over function fields. Journal of Number Theory 128 (2008) 3013-3030.
- AMS/MAA Joint Mathematics Meetings, January 2018.
- Budapest Semesters in Mathematics Education, Distinguished Visitor Program. February 20-23, 2017.
- Long Island Teacher Leadership Summit, January 12, 2017.