%CV.tex -- the ultimate CV LaTeX file, September 1999.1\documentclass[12pt]{article}2\newcommand{\myname}{William A.\ Stein}3\newcommand{\phone}{(510) 883-9938}4\newcommand{\email}{{\tt was@math.berkeley.edu}}5\newcommand{\www}{{\tt http://math.berkeley.edu/\~{\mbox{}}was}}6\newcommand{\address}{2041 Francisco Street, Apt.\ 14\\7Berkeley, CA 94709\\8USA}91011\textwidth=1.2\textwidth12\hoffset=-3em1314\usepackage{fancyhdr,ifthen}15\pagestyle{fancy}16\cfoot{} % no footers (in pagestyle fancy)17% running left heading18\lhead{{\bfseries\LARGE\em \noindent{}\hspace{-.2em}\myname{}}19\hfill \today{}\vspace{2ex}\\}20% running right heading21\rhead{\em {\small{\phone{}}} \,\,\,$\bullet$\,\,\, \email{} \,\,\,$\bullet$22\,\,\, \www{}\hspace{.67em}}23% adjust, because the header is now taller than usual.24\setlength{\headheight}{6ex}252627% bulleted list environment28\newenvironment{bulletlist}29{30\begin{list}31{$\bullet$}32{33\setlength{\itemsep}{0ex}34\setlength{\parsep}{0ex}35\setlength{\leftmargin}{1em}36\setlength{\parskip}{0ex}37\setlength{\topsep}{0ex}38}39}40{41\end{list}42}43%end newenvironment4445% bold sans-serif label for margin labels.46\newcommand{\marginlabel}[1]{\textsf{\textbf{#1}}}47%\newcommand{\marginlabel}[1]{\textsc{\textsc{#1}}}48\newcommand{\entrylabel}[1]{\mbox{\marginlabel{#1}}\hfill}4950\newcommand{\MainListlabel}[1]51{52\parbox[t]{\labelwidth}{\hspace{.8em}\marginlabel{#1}}53}5455% a list with fixed width marginlabels.56\newenvironment{MainList}[1]57{58\renewcommand{\entrylabel}{\MainListlabel}59\begin{list}{}60{61\renewcommand{\makelabel}{\entrylabel}62\setlength {\itemindent}{-.65em}63\setlength {\labelwidth}{#1}64\setlength {\leftmargin}{\labelwidth}65\setlength {\itemsep}{1ex}66}67}68{69\end{list}70}71%end newenvironment727374\begin{document}7576\begin{MainList}{104pt}7778\item [EDUCATION]79\begin{bulletlist}80\item {\bf University of California at Berkeley}\\81Ph.D., mathematics, expected May 2000.\\82{\bf Explicit approaches to modular abelian varieties}\vspace{-2ex}\\8384\item {\bf Northern Arizona University}, Flagstaff.\\85M.S. student, mathematics, 1994--1995.\\86B.S., mathematics, 1994.87\end{bulletlist}888990\item [AWARDS]91\begin{bulletlist}92\item Cal@SiliconValley university fellowship, 1999--2000.93\item Sarah M.\ Hallam department fellowship, Spring 1999.94\item Vice Chancellor research grant (computing equipment), 1999.95\item Graduate student researcher, Fall 1998.96\item Outstanding mathematics senior, 1994.97\item Applied math modeling contest, meritorious ranking, 1994.98\end{bulletlist}99100101\item [IN PROGRESS]102% Some of the following items can be obtained from\\103% \mbox{}104% \hspace{2em} {\tt http://shimura.math.berkeley.edu/\~{}was/Tables}105\begin{bulletlist}106\item {\em Lectures on Serre's conjectures},107with K.\thinspace{}A.~Ribet, to appear in the108IAS/Park City Mathematics Institute Lecture Series.109\item {\em Mod~$5$ approaches to modularity of icosahedral110Galois representations}, with K.\thinspace{}M.~Buzzard.111\item {\em Explicit approaches to modular abelian112varieties}, UC Berkeley Ph.D.\ thesis113under H.\thinspace{}W.~Lenstra.114\item {\em Hecke: The modular forms calculator}, computer software.115\item {\em The modular forms database:}\\116\mbox{}\hspace{3em}117{\tt http://shimura.math.berkeley.edu/\~{}was/Tables}118\item {\em Component groups of optimal quotients119of Jacobians}.120\item {\em Visibility of Shafarevich-Tate121groups of modular abelian varieties}, with A. Agash\'{e}.122\item {\em Computing analytic invariants of modular eigenforms},123with H.~Verrill.124\item {\em Lectures on modular forms and125Galois representations}, with K.\thinspace{}A. Ribet,126intended for Springer-Verlag's Universitext series.127\end{bulletlist}128129\item [PUBLICATIONS]130\begin{bulletlist}131\item {\em Empirical evidence for132the Birch and Swinnerton-Dyer conjectures for modular Jacobians of133genus 2 curves}, with E.\thinspace{}V.~Flynn, F.~Lepr\'{e}vost,134E.\thinspace{}F.~Schaefer,135M.~Stoll, J.\thinspace{}L.~Wetherell, submitted.136\item {\em Parity structures and generating functions from Boolean rings},137with D.\thinspace{}P.~Moulton, submitted.138\item {\em Fallacies, Flaws, and139Flimflam \#92: An Inductive Fallacy},140with A.~Riskin, College Math.\ Journal 26:5 (1995), 382.141\end{bulletlist}142143\newpage144\item [TEACHING]145{\bf NSF Sponsored IAS/Park City Mathematics Institute}146\begin{bulletlist}147\item {\em Teaching Assistant}, Summer 1999. Led problem sessions148and prepared notes for Ken Ribet's course on Serre's149conjectures for advanced number theory graduate students.150\end{bulletlist}151{\bf University of California at Berkeley}152\begin{bulletlist}153\item {\em Curriculum Development}, Fall 1997--Summer 1998. Developed154curriculum materials and {\sc Matlab} software for workshop based155calculus and linear algebra courses at UC Berkeley.156\item {\em Instructor}, Summer 1997. Taught discrete mathematics to157a class of 20--30 undergraduates. Duties included preparing and delivering158lectures, writing and grading exams, and conducting office hours.159\item {\em Teaching Assistant}, Fall 1995--Spring 1997.160Led discussion sections for the full range of undergraduate161linear algebra and calculus courses.162\item {\bf Evaluation average: 5.8 out of 7 from 300 students.}163\end{bulletlist}164{\bf Northern Arizona University}165\begin{bulletlist}166\item {\em Teaching}, 1994--1995. Taught two semesters167of college algebra and other freshman topics to a class168of 30--40 undergraduates.169Duties included all aspects of organizing a course, including170preparing and delivering lectures and grading examinations.171\end{bulletlist}172173\item [LECTURES]174\begin{bulletlist}175\item Delivered over twenty talks and organized graduate student176seminars on modular forms and abelian varieties177at UC Berkeley.178\item {\em Participant in panel discussion on the use of technology179in the classroom},180Park City Math.\ Inst., July, 1999.181\item {\em Demonstrations of number theory software},182Park City Math.\ Inst., July, 1999.183\item {\em Shafarevich-Tate groups of modular abelian varieties},184Park City Math.\ Inst., June, 1999.185\item {\em Shafarevich-Tate groups of modular abelian varieties},186Advances in Number Theory, Leiden, Netherlands, April, 1999.187\item {\em Visibility of Shafarevich-Tate groups},188Arizona Winter School, 1999.189\end{bulletlist}190191\item [COMPUTING]192Extensive experience with {\tt C++}, UNIX, {\sc Magma}, and PARI.193194\item [ADDRESS]195\address{}196197\item [PERSONAL]198US Citizen, born February, 1974.199200201\newpage202\item [REFERENCES]203\begin{bulletlist}204205206\item {\bf Kevin M. Buzzard}\\207{\em +44 207 594 8523}\\208Department of Mathematics\\209Huxley Building\\210Imperial College\\211180 Queen's Gate\\212London, SW7 2BZ\\213England\\214{\tt buzzard@ic.ac.uk}215\vspace{1ex}216\item {\bf Professor Robert Coleman}\\217{\em (510) 642-5101}\\218Department of Mathematics \#3840\\219University of California\\220Berkeley, CA 94720-3840\\221{\tt coleman@math.berkeley.edu}222\vspace{1ex}223\item {\bf Professor Hendrik W. Lenstra}\\224{\em (510) 643-7857}\\225Department of Mathematics \#3840\\226University of California\\227Berkeley, CA 94720-3840\\228{\tt hwl@math.berkeley.edu}229\vspace{1ex}230\item {\bf Professor Barry Mazur}\\231{\em (617) 495-2171 ext.~512}\\232Department of Mathematics\\233Harvard University\\234One Oxford Street\\235Cambridge, MA 02138\\236{\tt mazur@abel.math.harvard.edu}237\vspace{1ex}238\item {\bf Professor Lo\"\i{}c Merel}\\239{\tt merel@math.jussieu.fr}240\vspace{1ex}241\item {\bf Professor Kenneth A. Ribet}\\242{\em (510) 642-0648}\\243Department of Mathematics \#3840\\244University of California\\245Berkeley, CA 94720-3840\\246{\tt ribet@math.berkeley.edu}247\end{bulletlist}248249\newpage250\item [ABSTRACTS]251\begin{bulletlist}252\item {\em Lectures on Serre's conjectures (77 pages):}253This is an expository paper based on Ken Ribet's lectures at254the 1999 Park City Mathematics Institute; it will be255published in the conference proceedings.256257\item \vspace{1ex}{\em Mod~$5$ approaches to modularity of icosahedral258Galois \nobreak{representations} (16 pages):}259Consider a continuous odd irreducible representation260$\rho:\mbox{\rm Gal}(\overline{\mathbf{Q}}/\mathbf{Q})261\rightarrow\mbox{\rm GL}_2(\mathbf{C}).$262A special case of a general conjecture of Artin263is that the $L$-function $L(\rho,s)$ associated to~$\rho$264is entire.265Buzzard and I give new examples of representations~$\rho$ that satisfies266this conjecture. These were obtained by applying a recent267theorem of Buzzard and Taylor to a mod~$5$ reduction of~$\rho$,268combined with a computational verification of modularity of a269related mod~$5$ representation.270271\item \vspace{1ex}{\em Explicit approaches to modular abelian272varieties (130 pages):}273I give algorithms for computing on modular274abelian varieties of any dimension.275More precisely, I describe how to compute congruences, the modular degree,276the rational part of the special value of the $L$-function and277of its twists, the component group at primes of multiplicative278reduction, the period lattice, and the real and imaginary volumes.279There are still many invariants that I have not been able to280compute in all cases, including the exact structure of the torsion281subgroup and the regulator.282The second part of my thesis contains283investigations into several open problems, including284the Birch and Swinnerton-Dyer conjecture, Artin's conjecture285on complex Galois representations, and Serre's conjecture.286287\item\vspace{1ex} {\em Hecke: The modular forms calculator:}288Hecke is a {\tt C++} package for computing with spaces of modular forms289and modular abelian varieties.290I have been invited to visit the {\sc Magma} group in291Sydney in order to make Hecke a part of their computer292algebra system, and I have already ported my code to {\sc Magma}.293294\item\vspace{1ex} {\em The modular forms database:}295This is a collection of modular eigenforms,296special values of $L$-functions, arithmetic invariants of297modular abelian varieties, and other data.298These tables, which are freely299available on the Internet, have already been used300by many people.301302\item\vspace{1ex} {\em Component groups of optimal quotients of Jacobians (16 pages):}303Let~$A$ be an optimal quotient of~$J_0(N)$.304The main theorem of this paper gives a relationship between305the modular degree of~$A$ and the order of the component group306of~$A$. From this I deduce a computable formula for the307component group of any optimal \nobreak{quotient}308of~$J_0(N)$ at a prime of multiplicative309reduction. I then compute over one \nobreak{thousand}310examples leading me311to conjecture that the torsion and component groups of312quotients of $J_0(p)$ are as simple as possible.313314\item\vspace{1ex} {\em Visibility of Shafarevich-Tate315groups of modular abelian varieties (20 pages):}316We study Mazur's notion of visibility317of Shafarevich-Tate of modular \nobreak{abelian} varieties,318and use it to verify the conjecture of Birch and Swinnerton-Dyer319for several specific abelian varieties.320321\item\vspace{1ex} {\em Lectures on modular forms and322Galois representations (170 pages):} In 1996, Ken Ribet taught an323advanced course on modular forms and Galois representations.324In collaboration with Ribet, I am325turning my course notes into a book that is intended for326publication in Springer-Verlag's Universitext series.327328\item\vspace{1ex} {\em Empirical evidence for the Birch and329Swinnerton-Dyer conjecture for modular Jacobians330of genus~2 curves (22 pages):}331We provide systematic numerical evidence for the BSD conjecture332in the case of dimension two.333This conjecture relates six quantities associated to334a Jacobian over the rational numbers. One of these335quantities is the size~$S$ of the Shafarevich-Tate group.336Unable to compute~$S$ directly, we compute the five other337quantities and solve for the conjectural value~$S_?$ of~$S$.338For all 32~curves considered, the real number~$S_?$339is very close to either~$1$,~$2$, or~$4$, and340agrees with the size of the 2-torsion of the341Shafarevich-Tate group, which we could compute.342343\item\vspace{1ex} {\em Parity structures and generating functions from Boolean rings344\hspace{.2em}(8 pages):}345Let~$S$ be a finite set and~$T$ be a subset of the power set of~$S$.346Call~$T$ a {\em parity structure} for~$S$ if, for347each subset~$b$ of~$S$ of odd size, the number of subsets of~$b$348that lie in~$T$ is even. We classify parity structures using generating349functions from a free boolean ring.350We also show that if~$T$ is a parity structure, then, for each351subset~$b$ of~$S$ of even size, the number of subsets of~$b$ of352odd size that lie in~$T$ is even. We then give several other353properties of parity structures and discuss a generalization.354\end{bulletlist}355356357\end{MainList}358\end{document}359360361362363364365366367368369370371372%There are 9 lectures: Introduction to Serre's conjectures;373%The weak and strong conjectures; The weight in Serre's conjecture;374%Galois representations from modular forms; Introduction to level lowering;375%Approaches to level lowering; Mazur's principle; Level lower376%without multiplicity one; Level lowering with multiplicity one;377%Other directions.378379