BJORN POONEN

Department of Mathematics MIT Building 2-243 77 Massachusetts Ave. Cambridge, MA 02139-4307, USA Phone: (617)-258-8164 FAX: (617)-253-4358

                        e-mail: poonen@math.mit.edu
                  web page: http://math.mit.edu/~poonen/

LONG-TERM ACADEMIC POSITIONS Massachusetts Institute of Technology (2008– ) Professor. University of California at Berkeley (2004–2008) Professor. (2001–2004) Associate professor. (1997–2001) Assistant professor.

Princeton University (1995–97) Instructor and NSF postdoctoral fellow. Mathematical Sciences Research Institute, Berkeley (1994–95) Postdoctoral fellow.

VISITING POSITIONS Centre Interfacultaire Bernoulli, Lausanne, Switzerland (Summer and Fall 2012) Program co-organizer. Hausdorff Research Institute for Mathematics, Bonn, Germany (January-February 2009) Harvard University and MIT, Cambridge, Massachusetts (Fall 2007) Visiting scholar/professor. Isaac Newton Institute, Cambridge, England (June–July 2005) Institut Henri Poincaré, Paris (Fall 2004) Pacific Institute for the Mathematical Sciences, Vancouver (June–July 2004) Distinguished chair. Université Paris-Sud, Orsay, France (June 2001) Professeur invité. Isaac Newton Institute, Cambridge, England (Spring 1998) Rosenbaum fellow.

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

HONORS

• Teaching – MIT School of Science Prize in Undergraduate Teaching

• Professorships – Claude Shannon Professorship, 2009-2019.

– Miller Professorship, Fall 2005

• Fellowships

– Simons Fellow in Mathematics
– American Mathematical Society Fellow (inaugural class)
– American Academy of Arts and Sciences
– Guggenheim Fellowship
– Packard Fellowship
– Sloan Research Fellowship
– Rosenbaum Fellowship

– NSF Postdoctoral Fellowship

– Sloan Doctoral Dissertation Fellowship

– Office of Naval Research Graduate Fellowship

• Competitions

– Putnam Undergraduate Mathematics Competition: winner in 1985, 1986, 1987, and 1988 (one of eight four-time winners in the 70-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 participant (out of 380,000) to receive a

perfect score in 1985

• Other awards – The 2011 Chauvenet Prize

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

– Blumberg Creative Science Award

– The 1988-89 Wister Prize

– Phi Beta Kappa SELECTED INVITED LECTURES

• The Coven–Wood Lectures, Wesleyan, 2015.

• The Hedrick Lectures, MathFest, Portland, OR, 2014.

• Lecture series, Arizona Winter School, Tucson, 2014.

• The DePrima Lecture, Caltech, 2013.

• Plenary lecture, Canadian Number Theory Association meeting, Lethbridge, 2012.

• The 2012 Spring Lectures in Geometry, Ann Arbor, Michigan, 2012.

• Séminaire Bourbaki, Paris, 2012.

• Minicourse, Arithmetic Aspects of Rational Curves summer school, Grenoble, 2010.

• The Dressler Lecture, Manhattan, Kansas, 2010.

• Lecture series, Explicit Methods in Number Theory workshop, Oberwolfach, 2009.

• The Cantrell Lectures, Athens, Georgia, 2008.

• AMS invited address, Joint Mathematics Meetings, New Orleans, 2007.

• Lecture series, Clay Summer School in Arithmetic Geometry, Göttingen, 2006.

• Plenary lecture, Journées Arithmétiques, Marseille, 2005.

• Plenary lecture, Effective Methods in Algebraic Geometry, Alghero, 2005.

• Association of Symbolic Logic invited address, Joint Mathematics Meetings, Atlanta, 2005.

• Distinguished lecture series, Workshop on Computational Arithmetic Geometry, Vancouver, 2004.

• Lecture series, Explicit Methods in Number Theory trimester, Paris, 2004.

• Lecture series, Arizona Winter School, Tucson, 2003.

• Plenary lecture, Modular Forms and Abelian Varieties, Barcelona, 2002.

• Plenary lecture, Algorithmic Number Theory Symposium V, Sydney, 2002.

• The Beeger Lecture, 38th Nederlands Mathematisch Congres, Eindhoven, 2002.

• Plenary lecture, Millennial Conference on Number Theory, Urbana-Champaign, 2000.

• Plenary lecture, Foundations of Computational Mathematics, Oxford, 1999.

• Lecture series, Arizona Winter School, Tucson, 1998.

• Plenary lecture, Algorithmic Number Theory Symposium II, Bordeaux, 1996. GRADUATE STUDENTS SUPERVISED

• Kirsten Eisenträger, Ph.D. 2003.

• Patrick Corn, Ph.D. 2005.

• Dragos Ghioca, Ph.D. 2005. (co-supervised by Thomas Scanlon)

• Nghi Nguyen, Ph.D. 2005.

• Oscar Villareal, Ph.D. 2005.

• Bonnie Huggins, Ph.D. 2005.

• Greta Panova, M.A. 2006.

• Shahed Sharif, Ph.D. 2006.

• Aaron Greicius, Ph.D. 2007. (co-supervised by Hendrik Lenstra)

• David Zywina, Ph.D. 2008.

• Anthony Várilly-Alvarado, Ph.D. 2009.

• Bianca Viray, Ph.D. 2010.

• David Zureick-Brown, Ph.D. 2010.

• Kaloyan Slavov, Ph.D. 2011.

• Kęstutis Česnavičius, Ph.D. 2014.

• Jennifer Park, Ph.D. 2014.

• and five current Ph.D. students. POSTDOCTORAL FELLOWS SUPERVISED (most of these really supervised themselves)

• Hui June Zhu, Fall 1998 and 2000–2002.

• Nils Bruin, Fall 2000.

• Joseph Loebach Wetherell, Spring 2011.

• Ernest S. Croot III, 2001–2003.

• CheeWhye Chin, 2002–2003.

• Kevin Hare, 2002–2003.

• Andrew Snowden, 2010–2013.

• Yifeng Liu, 2012–2015.

• Tomer Schlank, 2012–2015.

• Stefan Patrikis, 2014–2015.

• Giacomo Micheli, Fall 2015.

• Holly Krieger, 2013–2016.

• Naoki Imai, 2015–2016. EDITORIAL POSITIONS

• Algebra & Number Theory, founding managing editor, 2006–present.

• Involve, editor, 2007–present.

• Journal of the American Mathematical Society, associate editor, 2000–2003 and 2004– 2010.

• A K Peters Research Notes in Mathematics book series, editorial board member, 2005–2014.

• International Mathematics Research Notices, editor, 2006–2008.

• London Mathematical Society Journal of Computation and Mathematics, editor, 2007–2011.

• Journal de Théorie des Nombres de Bordeaux, editor, 1998–2006.

• Journal of Number Theory, editor, 2003–2004. CONFERENCES I HAVE HELPED ORGANIZE

• Lehmer Conference, U. C. Berkeley, August 24–26, 2000, co-organizer with J. Brillhart, H. Lenstra, and H. Williams.

• MSRI semester on algorithmic number theory, Fall 2000, co-organizer with J. Buhler, C. Dwork, H. Lenstra, A. Odlyzko, and N. Yui.

• CMI Introductory Workshop in Algorithmic Number Theory, MSRI, August 14–23, 2000, co-organizer with D. Bailey, J. Buhler, C. Dwork, H. Lenstra, A. Odlyzko, W. Velez, and N. Yui.

• Arithmetic geometry, MSRI, December 11–15, 2000, chair of organizing committee consisting of N. Elkies, W. McCallum, J.-F. Mestre, and R. Schoof.

• Journées Arithmétiques XXII, July 2–6, 2001, Lille, France, member of scientific committee.

• Rational and integral points on higher-dimensional varieties, a workshop at the American Institute of Mathematics, Palo Alto, CA, December 11–20, 2002, co-organizer with Yu. Tschinkel.

• Arizona Winter School 2003 on “Logic and Number Theory”, a conference at the University of Arizona, Tucson, AZ, March 15–19, 2003, co-organizer with M. Kim and A. Pillay.

• Geometry and arithmetic over finite fields, a special session at the AMS meeting in San Francisco, May 3–4, 2003, co-organizer with J. Buhler.

• Algorithmic Number Theory Symposium VI (ANTS VI), June 13–18, 2004, member of program committee.

• An Introduction to Recent Applications of Model Theory, a workshop in the “Model Theory and Applications to Algebra and Analysis” program at the Isaac Newton Institute, March 29 to April 8, 2005.

• MSRI semester on “Rational and integral points on higher-dimensional varieties”, January 9 to May 19, 2006, member of organizing committee and chair of introductory workshop committee.

• MSRI Introductory Workshop on Rational and Integral Points on Higher-Dimensional Varieties, January 17–21, 2006, chair of organizing committee consisting of F. Bogomolov, J.- L. Colliot-Thélène, D. R. Heath-Brown, J. Kollár, A. Silverberg, Yu. Tschinkel.

• Arizona Winter School 2006 on “Computational and algorithmic aspects of algebra and arithmetic”, a conference at the University of Arizona, Tucson, AZ, March 11–15, 2006, coorganizer with F. Rodriguez-Villegas and D. Ulmer.

• Arithmetic geometry, an AMS special session at the Joint Math Meetings in New Orleans, January 8, 2007, co-organizer with M. Baker.

• Explicit methods for rational points on curves, a conference at the Banff International Research Station, February 4–9, 2007, co-organizer with N. Bruin.

• Berkeley Undergraduate Research Conference, April 7, 2007, co-organizer with a team of Berkeley undergraduates headed by Steven Sam.

• Modular forms and arithmetic, U. C. Berkeley and MSRI, June 28–July 2, 2008, coorganizer with Frank Calegari, Samit Dasgupta, and Richard Taylor.

• New methods in Hilbert’s 10th problem, Hausdorff Research Institute for Mathematics, February 9–13, 2009, co-organizer with Yuri Matiyasevich and Boris Moroz.

• Rational points on varieties, an AMS special session at the Joint Mathematics Meetings in Boston, January 5 and 6, 2012, co-organizer with Jennifer Balakrishnan, Bianca Viray, and Kirsten Wickelgren.

• BIRS summer school on contemporary methods for solving diophantine equations, co-organized with Michael Bennett, Nils Bruin, Yann Bugeaud, and Samir Siksek, Banff, June 10–17, 2012.

• Rational points and algebraic cycles, a semester-long program at the Centre Interfacultaire Bernoulli in Lausanne, Switzerland, July–December 2012, co-organizer with Hélène Esnault, Andrew Kresch, and Alexei Skorobogatov.

• Cohomological methods in arithmetic geometry, a workshop at the Universität Zürich during the Lausanne program above, co-organized with Hélène Esnault, Andrew Kresch, and Alexei Skorobogatov, September 10–14, 2012.

• Arithmetic of abelian varieties in families, a workshop during the Lausanne program above, co-organized with Hélène Esnault, Andrew Kresch, and Alexei Skorobogatov, November 12–16, 2012.

• Explicit methods in number theory, an Oberwolfach workshop, co-organized with Karim Belabas and Don B. Zagier, July 14–20, 2013.

• Connections between logic and arithmetic geometry, special session at MathFest, Portland, Oregon, August 7, 2014.

• Explicit methods in number theory, an Oberwolfach workshop, co-organized with Karim Belabas and Fernando Rodriguez–Villegas, July 5–11, 2015.

• Rational points, one of the seminars during the last week of the three-week Summer Institute

in Algebraic Geometry, University of Utah, July 27–31, 2015. SERVICE TO MIT

• Mathematics Council (hiring), 2013–2015.

• Freshman Advisor, 2013–2015.

• Mathematics Department Executive Committee, 2009–2015.

• Mathematics Major Advisor, 2009–present.

• Committee on Graduate Admissions, 2008–2015.

• Pure Mathematics Committee (hiring), 2008–2015.

• Mathematics Department Nominations Committee, 2008–2015.

• Mathematics Department Teaching Assignment Area Captain for Logic, 2008–present.

• Mathematics Department Graduate Co-chair, 2009–2012.

• Task Force on Improving Graduate Admissions Processes, 2011.

• Mathematics Department Education Committee, 2008–2009. SERVICE TO THE UNIVERSITY OF CALIFORNIA

• Mathematics Department Vice Chair for Undergraduate Affairs, 2006–2008.

• Mathematics Department Calculus and Course Committee, chair 2006–2007.

• Mathematics Department Preliminary Examination Committee, member 1998–2002 and chair 2002–2007.

• Academic Senate Committee on Computing and Communications, member 2006– 2008.

• Academic Senate Committee on Prizes, member 2000–2003 and chair 2003–2006.

• Mathematics Department Bowen Lectures Committee, co-chair 2002–2004.

• Mathematics Department Graduate Adviser, 2000–2003.

• Mathematics Department Chair Selection Committee, 1999 and 2002.

• Mathematics Department Non-Major Undergraduate Adviser, 1999–2001.

• various ad hoc committees, including the Hellman Family Faculty Fund Panel. OTHER PROFESSIONAL EXPERIENCE

• Center for Communications Research, Research on sorting and other mathematical algorithms.

• Lucent Technologies (6/96–7/96), Research in probabilistic packing and reservation under E. G. Coffman, Jr.

• 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.

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

• Mathematical Association of America (6/88–7/88 and 6/87–7/87) Assistant at the Math

Olympiad Program, under Cecil Rousseau. OTHER PROFESSIONAL ACTIVITIES

• AMS Committee to Select the Winner of the E. H. Moore Research Article Prize, 2012–2018 (chair 2014–2016).

• AMS Centennial Fellowship Committee, 2015–2017.

• Girls’ Angle Advisory Board, 2009–.

• Museum of Mathematics Advisory Council, 2008–.

• MAA Committee on the Putnam Prize Competition, 2008, 2009, 2010.

• AMS-MSRI Math Circle Library Advisory Board, 2007–.

• Mathematical Reviews, reviewer, 2006–2007.

• Berkeley Math Circle, 1998–2008.

• Zentralblatt für Mathematik und ihre Grenzgebiete, reviewer, 2001–2002.

• Committee on American Mathematics Competitions, 1989–2003 (duties included submitting and reviewing problems for the U. S. A. Mathematical Olympiad).

• Bay Area Mathematical Olympiad committee, 1998–2001.

• American Mathematical Monthly Problem Section, reviewer, 1996–1999. PUBLICATIONS

1. Generalized explicit descent and its application to curves of genus 3, with N. Bruin and M. Stoll, Forum Math. Sigma 4 (2016), e6, 80 pages.

2. The work of the 2014 Fields Medalists, with W. de Melo, J. Quastel, and A. Zorich, Notices Amer. Math. Soc. 62 (2015), no. 11.

3. Bertini irreducibility theorems over finite fields, with F. Charles, J. Amer. Math. Soc. 29 (2016), no. 1, 81–94.

4. Modeling the distribution of Selmer groups, Shafarevich–Tate groups, and ranks of elliptic curves, with M. Bhargava, D. Kane, H. Lenstra, and E. Rains, Cambridge J. Math. 3 (2015), no. 3, 275–321.

5. Computing Néron–Severi groups and cycle class groups, with D. Testa and R. van Luijk, Compositio Math. 151 (2015), 713–734.

6. Berkovich spaces embed in Euclidean spaces, with E. Hrushovski and F. Loeser, L’Enseignement Math. 60 (2014), no. 3-4, 273–292.

7. Undecidable problems: a sampler, pp. 211–241 in Interpreting Gödel: Critical essays, ed. J. Kennedy, Cambridge Univ. Press, 2014.

8. Most odd degree hyperelliptic curves have only one rational point, with M. Stoll, Annals of Math. 180 (2014), no. 3, 1137–1166.

9. p-adic interpolation of iterates, Bull. London Math. Soc. 46 (2014), no. 3, 525–527.

10. Average rank of elliptic curves (after Manjul Bhargava and Arul Shankar), Séminaire Bourbaki, Vol. 2011/2012, Exposés 1043-1058, Astérisque 352 (2013), Exp. No. 1049, 187–204.

11. Extending self-maps to projective space over finite fields, Doc. Math. 18 (2013), 1039–1044.

12. The method of Chabauty and Coleman, with W. McCallum, pp. 99–117 in: Explicit methods in number theory; rational points and diophantine equations, Panoramas et Synthèses 36, Société Math. de France, 2012.

13. Convergence of the restricted Nelder–Mead algorithm in two dimensions, with J. Lagarias and M. Wright, SIAM J. Optim. 22 (2012), 501–532.

14. Néron–Severi groups under specialization, with D. Maulik, Duke Math. J. 161 (2012), no. 11, 2167–2206.

15. Random maximal isotropic subspaces and Selmer groups, with E. Rains, J. Amer. Math. Soc. 25 (2012), no. 1, 245–269.

16. Self cup products and the theta characteristic torsor, with E. Rains, Math. Res. Letters 18 (2011), no. 06, 1305–1318.

17. Automorphisms mapping a point into a subvariety (with an appendix by Matthias Aschenbrenner), J. Alg. Geom. 20 (2011), 785–794.

18. Infinity: cardinal numbers, pp. 61–71 in Expeditions in mathematics (eds. T. Shubin, D. Hayes, G. Alexanderson), Math. Assoc. of America, 2011.

19. Curves over every global field violating the local-global principle, in the Proceedings of the Hausdorff Institute trimester on diophantine equations; Russian version: Zapiski Nauchnych Seminarov POMI 377 (2010), 141–147; English version: J. of Mathematical Sciences 171 (2010), no. 6, Springer, 782–785.

20. Multivariable polynomial injections on rational numbers, Acta Arith. 145 (2010), no. 2, 123– 127.

21. Insufficiency of the Brauer–Manin obstruction applied to étale covers, Annals of Math. 171 (2010), no. 3, 2157–2169.

22. The Brauer–Manin obstruction for subvarieties of abelian varieties over function fields, with J. F. Voloch, Annals of Math. 171 (2010), no. 1, 511–532.

23. Characterizing integers among rational numbers with a universal-existential formula, Amer. J. Math. 131 (2009), no. 3, 675–682.

24. Independence of points on elliptic curves arising from special points on modular and Shimura curves, II: local results, with A. Buium, Compositio Math. 145 (2009), no. 3, 566–602.

25. Existence of rational points on smooth projective varieties, J. Europ. Math. Soc. 11 (2009), no. 3, 529–543.

26. Independence of points on elliptic curves arising from special points on modular and Shimura curves, I: global results, with A. Buium, Duke Math. J. 147 (2009), no. 1, 181–191.

27. The set of nonsquares in a number field is diophantine, Math Res. Lett. 16 (2009), no. 1, 165–170.

28. Elliptic curves, pp. 183–207 in Algorithmic number theory: lattices, number fields, curves and cryptography (J. P. Buhler and P. Stevenhagen, eds.), Mathematical Sciences Research Institute publication 44, Cambridge University Press, 2008.

29. Isomorphism types of commutative algebras of finite rank over an algebraically closed field, Computational Arithmetic Geometry (edited by K. Lauter and K. Ribet), Contemporary Math. 463 (2008), Amer. Math. Soc., 111–120.

30. First-order characterization of function field invariants over large fields, with F. Pop, pp. 255– 271 of: Model Theory with applications to algebra and analysis, Volume 2 (edited by Z. Chatzidakis, H. D. Macpherson, A. Pillay, and A. J. Wilkie), London Mathematical Society Lecture Note Series 350, Cambridge University Press.

31. The moduli space of commutative algebras of finite rank, J. Europ. Math. Soc. 10 (2008), no. 3, 817–836.

32. Smooth hypersurface sections containing a given subscheme over a finite field, Math. Research Letters 15 (2008), no. 2, 265–271.

33. Undecidability in number theory^{1}, Notices Amer. Math. Soc. 55 (2008), no. 3, 344–350.

34. Gonality of modular curves in characteristic p, Math. Res. Letters 14 (2007), no. 4, 691–701.

35. Sieve methods for varieties over finite fields and arithmetic schemes, J. Théor. Nombres Bordeaux 19 (2007), 223–231.

36. Uniform first-order definitions in finitely generated fields, Duke Math. J. 138 (2007), no. 1, 1–21.

37. Twists of X(7) and primitive solutions to x^{2} + y^{3} = z^{7}, with E. Schaefer and M. Stoll, Duke Math. J. 137 (2007), no. 1, 103–158.

38. Heuristics for the Brauer–Manin obstruction for curves, Experimental Math. 15 (2006), no. 4, 415–420.

39. Diophantine definability of infinite discrete non-archimedean sets and Diophantine models over large subrings of number fields, with A. Shlapentokh, J. Reine Angew. Math. 288 (2005), 27– 47.

40. Finiteness theorems for modular curves of genus at least 2, with M. Baker, E. González-Jiménez, and J. González, Amer. J. Math. 127 (2005), 1325–1387.

1Awarded the 2011 Chauvenet Prize.

41. Orbits of automorphism groups of fields, with K. Kedlaya, J. of Algebra 293 (2005), no. 1, 167–184.

42. Unramified covers of Galois covers of low genus curves, Math. Res. Letters 12 (2005), no. 4, 475–481.

43. Multiples of subvarieties in algebraic groups over finite fields, Internat. Math. Res. Notices 2005, no. 24, 1487–1498.

44. Varieties without extra automorphisms III: hypersurfaces, Finite Fields and their Applications 11 (2005), no. 2, 230–268.

45. Bertini theorems over finite fields, Annals of Math. 160 (2004), no. 3, 1099–1127.

46. Everywhere ramified towers of global function fields, with I. Duursma and M. Zieve, pp. 148– 153 in: Finite fields and applications (G. Mullen, A. Poli, and H. Stichtenoth, eds.), 7th international conference, Fq7, Toulouse, France, May 5–9, 2003, Lecture Notes in Computer Science 2948, Springer-Verlag, 2004.

47. The conjugate dimension of algebraic numbers, with N. Berry, A. Dubickas, N. Elkies, and C. Smyth, Quarterly J. Math. 55 (2004), no. 3, 237–252.

48. Curves of every genus with many points, II: asymptotically good families, with N. Elkies, E. Howe, A. Kresch, J. Wetherell, and M. Zieve, Duke Math. J. 122 (2004), no. 2, 399–422.

49. Sums of values of a rational function, Acta Arith. 112.4 (2004), 333–343.

50. Arithmetic of higher-dimensional algebraic varieties, edited with Yu. Tschinkel, Progress in Math. 226 (2004), Birkhäuser.

51. Random diophantine equations, with J. F. Voloch, pp. 175–184 in: Arithmetic of higherdimensional algebraic varieties, B. Poonen and Yu. Tschinkel (eds.), Progress in Math. 226 (2004), Birkhäuser.

52. Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of ℚ, J. Amer. Math. Soc. 16 (2003), no. 4, 981–990. [MR1992832]

53. Squarefree values of multivariable polynomials, Duke Math. J. 118 (2003), no. 2, 353–373. [MR1980998]

54. Using elliptic curves of rank one towards the undecidability of Hilbert’s Tenth Problem over rings of algebraic integers, pp. 33–42 in: Algorithmic Number Theory, C. Fieker and D. Kohel (eds.), 5th International Symposium, ANTS-V, Sydney, Australia, July 2002, Proceedings, Lecture Notes in Computer Science 2369, Springer-Verlag, Berlin, 2002.

55. Computing rational points on curves, pp. 149–172 in: Number Theory for the Millennium III, M. A. Bennett et al. (eds.), A. K. Peters, Natick, Massachusetts, 2002. [MR1956273]

56. The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commentary (350 pages), with K. Kedlaya and R. Vakil, Math. Assoc. of America, 2002. [MR1933844]

57. The Grothendieck ring of varieties is not a domain, Math. Res. Letters 9 (2002), no. 4, 493–498. [MR 2003g:14010]

58. Random polynomials having few or no real zeros, with A. Dembo, Q. Shao and O. Zeitouni, J. Amer. Math. Soc. 15 (2002), 857–892. [MR 2003f:60092] 59. Computing torsion points on curves, Experimental Math. 10 (2001), no. 3, 449–465. [MR1917430]

(featured review)

60. The Hasse principle for complete intersections in projective space, pp. 307–311 in: Rational points on algebraic varieties, E. Peyre and Yu. Tschinkel (eds.), Progress in Math. 199 (2001), Birkhäuser. [MR 2002j:14028]

61. Spans of Hecke points on modular curves, Math. Res. Letters 8 (2001), no. 5–6, 767–770. [MR 2002k:11092]

62. Points having the same residue field as their image under a morphism, J. Algebra 243 (2001), 224–227. [MR 2002e:14002]

63. An explicit algebraic family of genus-one curves violating the Hasse principle, Proceedings of the 21st Journées Arithmétiques (Rome, 2001), J. Théor. Nombres Bordeaux 13 (2001), no. 1, 263–274. [MR 2002e:14036]

64. Torsion packets on curves, with M. Baker, Compositio Math. 127 (2001), no. 1, 109–116. [MR 2002d:14039]

65. Néron-Tate projection of algebraic points, Internat. Math. Res. Notices 2001, no. 9, 435–440. [MR 2002g:14065]

66. Zeros of Fekete polynomials, with B. Conrey, A. Granville, and K. Soundararajan, Ann. Inst. Fourier (Grenoble) 50 (2000), no. 3, 865–889. [MR 2001h:11108]

67. Genus-two curves with 22 torsion points, C. R. Acad. Sci. Paris, Sér. I Math. 330 (2000), 573–576. [MR 2001b:11058]

68. Large torsion subgroups of split Jacobians of curves of genus two or three, with E. Howe and F. Leprévost, Forum Math. 12 (2000), 315–364. [MR 2001e:11071]

69. Varieties without extra automorphisms II: hyperelliptic curves, Math. Res. Letters 7 (2000), no. 1, 77–82. [MR 2001g:14052b]

70. Varieties without extra automorphisms I: curves, Math. Res. Letters 7 (2000), no. 1, 67–76. [MR 2001g:14052a]

71. Lattice polygons and the number 12, with F. Rodriguez-Villegas, Amer. Math. Monthly 107 (2000), no. 3, 238–250. [MR 2001b:52022]

72. Algebraic families of nonzero elements of Shafarevich-Tate groups, with J.-L. Colliot-Thélène, J. Amer. Math. Soc. 13 (2000), no. 1, 83–99. [MR 2000f:11067]

73. The Cassels–Tate pairing on polarized abelian varieties, with M. Stoll, Annals of Math. 150 (1999), 1109–1149. [MR 2000m:11048] (featured review)

74. Reservation probabilities, with E. G. Coffman, Jr., and P. Jelenkovic, Advances in Performance Analysis 2 (1999), 129–158.

75. Computing call admission capacities in linear networks, with E. G. Coffman, Jr., A. Feldmann, and N. Kahale, Probab. Eng. Inform. Sc. 13 (1999), 387–406.

76. Mordell–Lang plus Bogomolov, Invent. Math. 137 (1999), no. 2, 413–425. [MR 2001c:11070]

77. A local-global principle for densities, with M. Stoll, Topics in Number Theory, S. D. Ahlgren et al. (eds.), Kluwer, 1999, 241–244. [MR 2000m:11048]

78. Packing random intervals on-line. Average-case analysis of algorithms, with E. G. Coffman, Jr., L. Flatto, and P. Jelenkovic, Algorithmica 22 (1998), no. 4, 448–476. [MR 2000h:60012] 79. Some diophantine equations of the form x^{n} +y^{n} = z^{m}, Acta Arith. LXXXVI.3 (1998), 193–205.

[MR 99h:11034]

80. Zeros of sparse polynomials over local fields of characteristic p, Math. Res. Lett. 5 (1998), 273–279. [MR 99f:11152]

81. The classification of preperiodic points of quadratic polynomials over ℚ: a refined conjecture, Math. Z. 228 (1998), no. 1, 11–29. [MR 99j:11076]

82. The number of intersection points made by the diagonals of a regular polygon, with M. Rubinstein, SIAM J. Discrete Math. 11 (1998), no. 1, 133–156. [MR 98k:52027]

83. Drinfeld modules with no supersingular primes, Internat. Math. Res. Notices 1998, no. 3, 151–159. [MR 99a:11074]

84. 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. [MR 98j:11048]

85. Explicit descent for Jacobians of cyclic covers of the projective line, with E. F. Schaefer, J. Reine Angew. Math. 488 (1997), 141–188. [MR 98k:11087] (featured review)

86. Torsion in rank 1 Drinfeld modules and the uniform boundedness conjecture, Math. Ann. 308 (1997), 571–586. [MR 98h:11073]

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

88. 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. [MR 98m:94049]

89. 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]

90. 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. [MR 97m:94010]

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PREPRINTS (copies available upon request) • Galois points on varieties, with M. Jarden, accepted by J. Ramanujan Math. Soc.

• Uniform boundedness of rational points and preperiodic points, submitted.

• The moduli space of rings, submitted to the Proceedings of the 2014 Séminaire de Mathématiques Supérieures at the Centre de Recherches Mathématiques.

• Automorphisms of Harbater–Katz–Gabber curves, with F. Bleher, T. Chinburg, and P. Symonds, submitted.

• A heuristic for boundedness of ranks of elliptic curves, with J. Park, J. Voight, and M. Wood, submitted.

• A computable functor from graphs to fields, with R. Miller, H. Schoutens, and A. Shlapentokh, submitted.

• Abelian varieties isogenous to a power of an elliptic curve, with B. Jordan, A. Keeton, E. Rains, N. Shepherd-Barron, and J. Tate, submitted.

• Unique factorization of principally polarized abelian varieties, with B. Jordan and A. Keeton, submitted.

• The analytic class number formula for orders in products of number fields, with B. Jordan, preprint.

• Rational points on varieties, book.