William A. Stein Curriculum Vitae

·  was@math.harvard.edu  ·  http://math.harvard.edu/˜ was

Education · University of California at Berkeley Ph.D., mathematics, May 2000. · Northern Arizona University, Flagstaff, Arizona M.S. student, mathematics, 1994–1995. B.S., mathematics, computer science minor, 1991–1994.

Dissertation · Explicit approaches to modular abelian varieties Committee: Hendrik W. Lenstra (Chair), Bjorn Poonen, Bin Yu.

Awards · Harvard University, NSF Postdoc under Mazur, Fall 2000–present. · Clay Mathematics Institute Liftoff Fellow, Summer 2000. · Cal@SiliconValley University Fellowship, 1999–2000. · Sarah M. Hallam Department Fellowship, Spring 1999. · Vice Chancellor Research Grant, 1999. · Graduate Student Researcher, Fall 1998. · Outstanding Mathematics Senior, 1994. · Applied math modeling contest, meritorious ranking, 1994.

Publications · Mod 5 approaches to modularity of icosahedral Galois representations (18 pages), with K. Buzzard, to appear in Pacific J. of Math. · Lectures on Serre’s conjectures (91 pages), with K. A. Ribet, to appear in the IAS/Park City Mathematics Institute Lecture Series. · Component groups of quotients of J_{0}(N) (8 pages), with D. Kohel, ANTS IV proceedings, 2000. · Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves (22 pages), with E. V. Flynn, F. Leprévost, E. F. Schaefer, M. Stoll, J. L. Wetherell, to appear in Math. of Comp. · Parity structures and generating functions from Boolean rings (8 pages), with D. P. Moulton, submitted. · Fallacies, Flaws, and Flimflam #92: An Inductive Fallacy (1 page), with A. Riskin, College Math. J. 26:5 (1995), 382.

In progress · Lectures on modular forms and Galois representations

William A. Stein Curriculum Vitae

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(170 pages), with K. A. Ribet, intended for publication in the Springer-Verlag Universitext series. · The field generated by the points of small prime order on an elliptic curve (5 pages), with L. Merel. · Visibility of Shafarevich-Tate groups of modular abelian varieties (20 pages), with A. Agashe. · Component groups of optimal quotients of Jacobians. · Indexes of genus one curves (10 pages).

Computer skills · Author of the modular symbols part of Magma.

· Author of Hecke: A Modular Forms Calculator · The modular forms database, created using Hecke:

        http://shimura.math.berkeley.edu/~was/Tables/.

· C++, HTML, L^{A}TEX, Magma, Matlab, PARI, and UNIX.

Seminars · Getting your hands on modular forms using modular symbols, MSRI, Berkeley, CA, invited, August 2000. · Visibility of Shafarevich-Tate groups, Durham, England, invited, Summer 2000. · Modularity of icosahedral Galois representations, Copenhagen, Denmark, invited, Summer 2000. · Visibility of Shafarevich-Tate groups, Utrecht, Holland, invited, Summer 2000. · Three curves: A story of congruences, multiplicity one, and visibility of Shafarevich-Tate groups, Workshop zur Arithmetischen Geometrie, Inst. fur Exp. Math., Essen, Germany, invited, Summer 2000. · Computing with modular forms, UC Berkeley mentor lecture, invited, Spring 2000. · Evidence for Tate’s generalization of the Birch and Swinnerton-Dyer Conjecture, University of Texas, invited, Spring 2000. · Organized the graduate student number theory seminar, and gave talks on Component groups of quotients of J_{0}(N), Fall 1999. · The Manin index of optimal quotients of J_{0}(N), Berkeley Number Theory Seminar, Fall 1999. · A modular icosahedral Galois representation of conductor 2^{5} · 43,

·  was@math.harvard.edu  ·  http://math.harvard.edu/˜ was

Berkeley Number Theory Seminar, Fall 1999. · Shafarevich-Tate groups of modular abelian varieties, IAS/Park City Math. Inst., June, 1999. · Shafarevich-Tate groups of modular abelian varieties, Advances in Number Theory, Leiden, Netherlands, April, 1999. · Visibility of Shafarevich-Tate groups, Arizona Winter School, 1999. · The BSD conjecture, Graduate Student Colloquium, Spring 1999. · A series of talks on Ramakrishna’s deformation theory of Galois representations, Ribet’s Fall 1998 seminar. · Finite flat groups schemes of type (p, p, …), Spring 1998. · Kolyvagin’s Euler system of Heegner points, Buzzard’s Seminar, Berkeley, Spring 1997. · Organized the Abelian Varieties Seminar, Berkeley, Spring 1996.

Service Refereed papers for Mathematische Annalen and Journal of Symbolic Computation.

Teaching NSF Sponsored IAS/Park City Mathematics Institute · Teaching Assistant, Summer 1999. Led problem sessions and prepared notes for Ken Ribet’s course on Serre’s conjectures for advanced number theory graduate students. · Participated in a panel discussion on the use of technology in the classroom. · Led workshops on the number theory software PARI and Hecke.

University of California at Berkeley · Curriculum Development, Fall 1997–Summer 1998. Developed curriculum materials and Matlab software for workshop-based calculus and linear algebra courses at UC Berkeley. · Instructor, Summer 1997. Taught discrete mathematics to a class of 20–30 undergraduates. Duties included preparing and delivering lectures, writing and grading exams, and conducting office hours. Evaluation average: 6.1 out of 7. · Teaching Assistant, Fall 1995–Spring 1997. Led discussion sections for linear algebra and second and third semester calculus courses.

·  was@math.harvard.edu  ·  http://math.harvard.edu/˜ was

Northern Arizona University · Teaching, 1994–1995. Taught four complete undergraduate courses, two on college algebra and two on other freshman topics. Duties included all aspects of organizing a course, including preparing and delivering lectures and grading examinations.

Memberships · American Mathematical Society, 1995–present. · Mathematical Association of America, 1998–present.

Address 345 Harvard Street, Apt. 4D Cambridge, MA 02138 USA Email: was@math.harvard.edu

Personal US Citizen, born February 21, 1974

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References

Doctor Kevin M. Buzzard Department of Mathematics Huxley Building Imperial College 180 Queen’s Gate London, SW7 2BZ England +44 207 594 8523 buzzard@ic.ac.uk Professor Robert F. Coleman Department of Mathematics #3840 University of California Berkeley, CA 94720-3840

(510) 642-5101

coleman@math.berkeley.edu

Professor Hendrik W. Lenstra Department of Mathematics #3840 University of California Berkeley, CA 94720-3840

(510) 643-7857 hwl@math.berkeley.edu Professor Barry C. Mazur Department of Mathematics Harvard University One Oxford Street Cambridge, MA 02138

(617) 495-2171 ext. 512

mazur@abel.math.harvard.edu

Professor Loïc Merel Paris France merel@math.jussieu.fr Professor Kenneth A. Ribet Department of Mathematics #3840 University of California Berkeley, CA 94720-3840

(510) 642-0648

ribet@math.berkeley.edu