Sharedwww / nsf / biographical_sketch.texOpen in CoCalc
\newcommand{\thisdocument}{Biographical Sketch}


\head{Professional Preparation}%
  % 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 \\

\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.

\head{Most Relevant Publications}%
\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.%

\head{Other Publications}%
\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.%

\head{Synergistic Activities}
\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
\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
 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).

\head{Collaborators and Other Affiliations}
\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:}
\item {\bf Ph.D. adviser:} Hendrik Lenstra, University of Leiden,
\item {\bf NSF Postdoctoral adviser:} Barry Mazur, Harvard
\item \textbf{Thesis:} Advised three undergraduate thesis at