BJORN POONEN

Department of Mathematics 3840 University of California Berkeley, CA 94720-3840, USA Phone: (510)-642-5229 FAX: (510)-642-8204

                    e-mail: poonen@math.berkeley.edu

POSITIONS HELD

University of California at Berkeley (1997–present except spring 1998) Assistant professor. Newton Institute (spring 1998) Rosenbaum fellow. Princeton University (1995–97) Instructor and NSF postdoctoral fellow. Mathematical Sciences Research Institute, Berkeley (1994–95) Postdoctoral fellow.

EDUCATION

Ph. D., Mathematics, University of California at Berkeley, 1994. A. B., Mathematics and Physics, Harvard, 1989, summa cum laude.

HONORS

• Fellowships – Sloan Research Fellowship

– Rosenbaum Fellowship

– NSF Postdoctoral Fellowship

– Sloan Doctoral Dissertation Fellowship

– Office of Naval Research Graduate Fellowship

– NSF-NATO Postdoctoral Fellowship (declined)

– NSF Graduate Fellowship (declined)

– Mobil Fellowship (declined)

• Competitions

– Putnam Undergraduate Mathematics Competition: winner in 1985, 1986, 1987, and 1988 (one of four four-time winners in the 60-year history of the competition)

– International Mathematical Olympiad: silver medalist in 1985 (while on the 6-person U. S. team)

– U. S. A. Mathematical Olympiad: winner in 1985

– American High School Mathematics Exam: only student in U. S. to receive a perfect score

in 1985

• Other Awards – Thomas T. Hoopes Prize (for an undergraduate thesis written under J. Tate)

– Blumberg Creative Science Award

– The 1988-89 Wister Prize

– Phi Beta Kappa OTHER PROFESSIONAL EXPERIENCE

• Center for Communications Research (7/96–8/96, 5/93–8/93, 5/90–8/90, 12/89–1/90, and 6/89–8/89) Research on sorting and other mathematical algorithms.

• AT&T (6/96–7/96, 5/94–8/94, 5/92–8/92, and 7/87–9/87) Research in combinatorics and number theory under Andrew M. Odlyzko.

• Univ. of Minn. at Duluth (7/88–9/88) Research on combinatorial problems under Joseph A. Gallian.

• Mathematical Assoc. of America (6/87–7/87 and 6/88–7/88) Assistant at the Math Olympiad Program, under Cecil Rousseau.

PROFESSIONAL ACTIVITIES

• Committee on American Mathematics Competitions, member from 1989 to present (duties include submitting and reviewing problems for the U. S. A. Mathematical Olympiad)

• American Mathematical Monthly Problem Section, reviewer.

• Massachusetts Association of Mathematics Leagues, author of the second level examination of the Olympiad in 1988.

PUBLICATIONS

• Zeros of sparse polynomials over local fields of characteristic p, Math. Res. Letters. 5 (1998), 273–279.

• The classification of preperiodic points of quadratic polynomials over ℚ: a refined conjecture, Math. Zeit. 228 (1998), no. 1, 11–29.

• Drinfeld modules with no supersingular primes, Internat. Math. Res. Notices 1998, no. 3, 151–159.

• The number of intersection points made by the diagonals of a regular polygon, with M. Rubinstein, SIAM J. on Discrete Math. 11 (1998), no. 1, 133–156.

• Explicit descent for Jacobians of cyclic covers of the projective line, with E. F. Schaefer, J. Reine Angew. Math. 488 (1997), 141–188.

• Cycles of quadratic polynomials and rational points on a genus-2 curve, with E. V. Flynn and E. F. Schaefer, Duke Math. J. 90 (1997), 435–463.

• Torsion in rank 1 Drinfeld modules and the uniform boundedness conjecture, Math. Ann. 308 (1997), 571–586.

• A 2-adic approach to the analysis of cyclic codes, with A. R. Calderbank and W. Li, IEEE Trans. Inform. Th. 43 (1997), 1–11.

• How to spread rumors fast, with C. K. Fan and G. Poonen, Math. Mag. 70 (1997), 40–46.

• Sous-groupes de torsion d’ordres éléves de jacobiennes décomposables de courbes de genre 2, with E. Howe and F. Leprévost, C. R. Acad. Sci. Paris, Sér. I Math. 323 (1996), 1031–1034. [MR 97k:11097]

• Computational aspects of curves of genus at least 2, pp. 283–306 in: Cohen, H. (ed.), Algorithmic Number Theory, Second International Symposium, ANTS-II, Talence, France, May 1996, Proceedings, Lecture Notes in Computer Science 1122, Springer-Verlag, Berlin. [MR 98c:11059]

• Fractional power series and pairings on Drinfeld modules, J. Amer. Math. Soc. 9 (1996), no. 3, 783–812. [MR 96j:11081]

• On a conjecture of Helleseth regarding pairs of binary m-sequences, with A. R. Calderbank, G. McGuire, and M. Rubinstein, IEEE Transactions on Information Theory 42 (1996), 988–990.

• Local height functions and the Mordell-Weil theorem for Drinfeld modules, Compositio Math. 97 (1995), 349–368. [MR 96k:11075]

• Rigidity and semi-invariants in Drinfeld modules, J. Numb. Th. 55 (1995), 181–196. [MR 97e:11066]

• Packing random intervals, with E. J. Coffman and P. Winkler, Prob. Theory Relat. Fields 102 (1995), 105–121. [MR 96h:60016]

• Congruences relating the order of a group to the number of conjugacy classes, Amer. Math. Monthly 105 (1995), 440–442.

• Parking arcs on the circle with applications to one-dimensional communication networks, with E. Coffman, Jr. and C. Mallows, Ann. of Applied Prob. 4 (1994), 1098–1111. [MR 95k:60245]

• The processor minimization problem with independent waiting time constraints, with E. Coffman, Jr., L. Flatto, and P. Wright, Theoret. Comput. Sci. 125 (1994), 3–16. [MR 94k:68014] • The zeta function of the beta transformation, with L. Flatto and J. Lagarias, Ergodic Th. &

Dynam. Sys. 14 (1994), 237–266. [MR 95c:58141]

• Zeros of polynomials with 0,1 coefficients, with A. Odlyzko, L’Enseign. Math. 39 (1993), 317–348. [MR 95b:11026]

• Maximally complete fields, L’Enseign. Math. 39 (1993), 87–106. [MR 94h:12005]

• The worst case in Shellsort and related algorithms, J. Algorithms 15, No. 1 (July 1993), 101–124. [MR 94j:68044]

• Improved lower bounds for Shellsort, with C. Greg Plaxton and Torsten Suel, Proc. 33^{rd} IEEE Foundations of Computer Science Symp., 226–235.

• Union-closed families, J. Combin. Theory Ser. A 59, No. 1 (Mar. 1992), 253–268. [MR 93a:05005]

• Periodicity of a combinatorial sequence, Fibonacci Quart. 26, No. 1 (Feb. 1988), 70–76. [MR

89g:05007] PREPRINTS (copies available upon request)

• Some diophantine equations of the form x^{n} + y^{n} = z^{m}, accepted by Acta Arith.

• Packing random intervals on-line, with E. G. Coffman, Jr., L. Flatto, and P. Jelenkovic, accepted by Algorithmica.

• A local-global principle for densities, with M. Stoll, accepted by Topics in Number Theory conference proceedings, Kluwer.

• Large torsion subgroups of split Jacobians of curves of genus two or three, with E. Howe and F. Leprévost, submitted.

• The Cassels-Tate pairing on polarized abelian varieties, with M. Stoll, submitted.

• Reservation probabilities, with E. G. Coffman, Jr., and P. Jelenkovic, submitted.

• Mordell-Lang plus Bogomolov, submitted.

• Mordell-Lang plus Bogomolov II: the division group, preprint, 1998.

• Zeros of Fekete polynomials, with A. Granville and B. Conrey, in preparation.

• Computing call admission capacities in linear networks, with E. G. Coffman, Jr., A. Feldmann, and N. Kahale, in preparation.

• Nelder-Mead in 2D, with J. Lagarias and M. Wright, in preparation.

• Lattice polygons and the number 12, with F. Rodriguez-Villegas, in preparation.

• Algebraic families of nonzero elements of Shafarevich-Tate groups, with J.-L. Colliot-Thélène, in preparation.