\documentclass[11pt]{article} \include{macros} \newcommand{\thisdocument}{Biographical Sketch} \begin{document} %\maketitle \head{Professional Preparation}% \begin{center} \begin{tabular}{lll} % after \\: \hline or \cline{col1-col2} \cline{col3-col4} ... \mbox{}\hspace{4.2ex}& Northern Arizona University\hspace{1.03in}\mbox{}& Mathematics, B.S. 1994 \\ & University of California at \textbf{Berkeley} & Mathematics, Ph.D. 2000 \\ & \textbf{Harvard University} & NSF postdoc, 2000--04 \\ \end{tabular} \end{center} \head{Appointments}% \begin{itemize} \item Benjamin Peirce Assistant Professor of Mathematics, % Harvard University, July 2001--May 2005% \item NSF Postdoctoral Research Fellowship % under Barry Mazur at Harvard University, August 2000--May 2004.% \item Clay Mathematics Institute Liftoff Fellow, Summer 2000. \end{itemize} \head{Most Relevant Publications}% \begin{itemize} \item {\ptitle Visible Evidence for the Birch and Swinnerton-Dyer Conjecture for Rank 0 Modular Abelian Varieties} (31 pages), with A.~Agashe, to appear in Mathematics of Computation.% \item {\ptitle Visibility of Shafarevich-Tate Groups of Abelian Varieties}, (19 pages), with A.~Agashe, J. Number Theory, {\bf 97} (2002), no. 1, 171--185.% \item {\ptitle Studying the Birch and Swinnerton-Dyer Conjecture for Modular Abelian Varieties Using MAGMA} (22 pages), to appear as a chapter in the Springer-Verlag book ``Computational Experiments in Algebra and Geometry''.% \item {\ptitle Constructing Elements in Shafarevich-Tate Groups of Modular Motives}, (19 pages) with N.~Dummigan and M.~Watkins, to appear in ``Number theory and algebraic geometry---to Peter Swinnerton-Dyer on his 75th birthday'', Ed. by M. Reid and A. Skorobogatov.% \item {\ptitle $J_1(p)$ Has Connected Fibers} (77 pages), with B.~Conrad and S.~Edixhoven, to appear in Documenta Mathematica.% \end{itemize} \head{Other Publications}% \begin{itemize} \item {\ptitle Shafarevich-Tate Groups of Nonsquare Order} (13 pages), to appear in the Barcelona MCAV proceedings, Ed. by Jordi Quer.% \item {\ptitle Mod~$5$ Approaches to Modularity of Icosahedral Galois Representations} (18 pages), with K.~Buzzard, Pacific J. Math, {\bf 203} (2002), no. 2, 265--282.% \item {\ptitle There are Genus One Curves over $\mathbf{Q}$ of Every Odd Index} (9 pages), J. Reine Angew. Math. (Crelle's Journal), {\bf 547} (2002), 139--147.% \item {\ptitle Component Groups of Purely Toric Quotients of Semistable Jacobians}, (20 pages), with B.~Conrad, Math. Res. Lett., {\bf 8} (2001), no. 5-6, 745--766.% \item {\ptitle The Field Generated by the Points of Small Prime Order on an Elliptic Curve} (7 pages), with L.~Merel, Internat.\ Math.\ Res.\ Notices (2001), no.~20, 1075--1082.% \end{itemize} \head{Synergistic Activities} \begin{itemize} \item {\bf Databases:} Created and maintain the Modular Forms Database. This is over 40GB of continually expanding data about modular forms and abelian varieties, which is freely available online: \begin{center} {\sf http://modular.fas.harvard.edu/Tables/}.% \end{center} \item {\bf Research Tools:} Author of the modular forms and modular symbols parts of the {\sc Magma} computer algebra system (425 pages (26000 lines) of code plus documentation). This is a tool used by mathematicians who do computations with modular forms.% \item {\bf Outside Service:} Defense Science Study Group member 2002--2003: DSSG is a DARPA funded program administered by the Institute for Defense Analysis; wrote classified paper on GPS vulnerabilities. \item {\bf Outreach:} Canada/USA MathCamp mentor (2002); Several Math Circles talks in Boston; Guest speaker at Harvard/MIT math competition (2001). \end{itemize} \head{Collaborators and Other Affiliations} \newcommand{\hl}[1]{#1}% \begin{itemize} \item \textbf{Coauthors:} A.~\hl{Agashe} (Univ.~of Missouri), K.~\hl{Buzzard} (Imperial College, London), R.~\hl{Coleman} (UC Berkeley), B.~\hl{Conrad} (Univ.~of Michigan), N.~\hl{Dummigan} (Sheffield, UK), S.~\hl{Edixhoven} (Leiden, Netherlands), F.~\hl{Lepr\'evost} (Univ.\ Joseph Fourier, Technische Univ.\ Berlin), E.\thinspace{}V. Flynn (Liverpool, UK), D.~\hl{Kohel} (Univ.~of Sydney), L.~\hl{Merel} (Paris 6), K.~\hl{Ribet} (UC Berkeley), E.\thinspace{}F.~\hl{Schaefer} (Santa Clara Univ.), M.~\hl{Stoll} (Inter.~Univ.~Bremen, Germany), H.\thinspace{}A.~\hl{Verrill} (Louisiana State), M.~\hl{Watkins} (Penn. State Univ.), J.\thinspace{}L.~\hl{Wetherell} (CCR, San Diego)% \item \textbf{Graduate and Postdoctoral Advisors:} \begin{itemize} \item {\bf Ph.D. adviser:} Hendrik Lenstra, University of Leiden, Netherlands.% \item {\bf NSF Postdoctoral adviser:} Barry Mazur, Harvard University. \end{itemize} \item \textbf{Thesis:} Advised three undergraduate thesis at Harvard. \end{itemize} \end{document}