JOSE´ FELIPE VOLOCH BIOGRAPHICAL DATA

EDUCATION Ph.D. University of Cambridge, UK 1985 Cert. Advanced studies in Math., University of Cambridge 1983 M.Sc. IMPA, Rio de Janeiro, Brazil 1982 PROFESSIONAL EXPERIENCE 2000- Professor, Department, University of Texas at Austin. Jan-Jun 1998 Research Professor, Mathematical Sciences Research Institute. 1995-2000 Associate Professor, Mathematics Department, University of Texas at Austin. 1992-95 Assistant Professor, Mathematics Department, University of Texas at Austin. 1991-92 Visiting Scholar, University of California, Berkeley. 1991-92 Associate Professor, IMPA, Rio de Janeiro, Brazil. 1985-91 Assistant Professor, IMPA, Rio de Janeiro, Brazil. COURSES TAUGHT Course Title M408C Differential and Integral M408D Sequences, Series and Multivariate Calculus M308M Multivariable Calculus M325K M343K Introduction to Algebraic Structures M373K Algebraic Structures I M328K M390C Diophantine M390C Algebraic M390C Algebraic Functions M343K Introduction to Algebraic Structures M390C M380D M390C p-adic numbers M343K Introduction to Algebraic Structures M390C Applied Number Theory M375 Mathematics of Information Transmission M380C Algebra M390C Differential Algebra M343L Applied Number Theory M390C Equations over finite fields M390C Discrete Mathematics M375 Applications of Finite Fields M390C Exponential Sums M390C M375 Computational Number Theory

August 19, 2010 Jos´eFelipe Voloch Page 2

M390C Algorithms for Finite Fields GRADUATE STUDENT SUPERVISION AND COMMITTEE PARTICIPATION Ph.D. Degrees Supervised Amilcar Pacheco (1986-1989) “Generalized Hasse-Witt invariants on algebraic curves” Antonios Broumas (1993-1995) “p-descent in characteristic p” Cong Kang (1996-1999) “On Lang’s Conjecture for Surfaces of General Type” Sangtae Jeong (1996-1999) “Diophantine problems in function fields of positive characteristic” Luis Renato Abib Finotti (1997-2001) “Canonical and minimal degree liftings of curves” Ana R. B. Neira (1998-2002) “Power series in p-adic roots of unity” Francisco X. Portillo Bobadilla (2000-2004) “Computations of an equation of the Birch and Swinnerton- Dyer type” Marcos A. Zarzar (2001-2006) “Error-Correcting codes on low N´eron-Severi rank surfaces” David C. Jedlicka (2002-2006) “On the suitability of power functions as S-boxes for symmetric cryptosystems” Laura Hitt, (2002-2007) “Genus two curves in pairing based cryptography and the minimal embed- ding field” Rohit Ghosh, (2004-2007) “Incompleteness of the Giulietti-Ughi arc for Large Primes” Phillipa Charters (2005-2009) “Generalizing binary quadratic residue codes to higher power residues over larger fields” Herivelto Borges (2005-2009) “Characterization of multi-Frobenius non-classical curves and construction of complete plane (N, d)-arcs” Ricardo Concei¸c˜ao(2004-2009) “Twists of Elliptic curves with a large set of integral points over Fq(t)” Current PhD students Chia-Liang Sun Master’s Degrees Supervised Jorge Aar˜ao(1988-1989) “Primes in progressions” Tae Wan Park (1995-1996) “A study of the asymptotically good towers of function fields” Aby Bentata Goldenberg (2003-2004) “Exponential Factorization Methods” Brendan Younger (2006-2007) “Finding elements of large order in finite fields” Petar Ivanov (2007-2008) “Efficient attack against the algebraic surface public-key cryptosystem” PUBLICATIONS Articles 1. (with J. M. Gomes) Une in´egalit´eg´eometriqueconcernent les points critiques d’une fonction. C. R. Acad. Sci. Paris 295(1982), 535-537. 2. (with D. Koutrofiotis) Saddle surfaces admitting local support planes. J. Reine Angew. Math. 385(1985), 1-5. 3. equations over function fields. Bol. Soc. Brasil. Mat. 16(1985), 29-39. 4. (with K.-O. St¨ohr)Weierstrass points and curves over finite fields. Proc. London Math. Soc. (30) 52(1986), 1-19. 5. On the completeness of certain place arcs. European J. 8(1987), 453-456. 6. On plane arcs over prime fields. J. Geometry 35(1990), 198-200. 7. (with K. O. St¨ohr)A formula for the Cartier operator on plane algebraic curves. J. Reine Angew. Math. 377(1987), 49-64. Jos´eFelipe Voloch Page 3

8. Diophantine approximation in positive characteristic. Periodica Math. Hungarica 19(1988), 217- 225. 9. A note on algebraic curves in characteristic two. Comm. Algebra 16(4)(1988), 869-875. 10. A note on elliptic curves over finite fields. Bull. Soc. Math. France 116(1988), 455-458. 11. (with J. Hirschfeld) The characterization of elliptic curves over finite fields. J. Australian Math. Soc. Ser. A 45(1988), 275-286. 12. (with A. Garcia) Wronskians and linear independence in prime characteristic. Manuscripta Math. 59(1987), 457-469. 13. On the number of values taken by a polynomial over a finite field. Acta Arithmetica LII(1989), 197-201. 14. (with I. Vainsencher) On the Castelnuovo-Severi inequality. J. Reine Angew. Math. 390(1988), 114-116. 15. (with A. Garcia) Fermat curves over finite fields. J. Number Theory 30(1988), 345-356. 16. (with A. Hefez) Frobenius non-classical curves. Arch. Math. (Basel) 54(1990), 263-273. 17. On the geometry of space curves. Proc. of the 10th School of Algebra, IMPA, Rio de Janeiro, 1990, pp.121-122. 18. On the completeness of certain plane arcs II. European J. Combinatorics 11(1990), 491-496. 19. Mordell’s equation in characteristic three. Bull. Australian Math. Soc. 47(1990), 149-150. 20. Explicit p-descent for elliptic curves in characteristic p. Compositio Math. 74(1990), 247-258. 21. Primitive points on constant elliptic curves over function fields. Bol. Soc. Brasil. Mat. 21(1990), 91-94. 22. A diophantine problem on algebraic curves over function fields of positive characteristic. Bull. Soc. Math. France, 119(1991), 121-126. 23. Complete arcs in Galois planes of non- order, in Advances in Finite and Designs, J. Hirschfeld, D. Hughes and J. Thas, eds., Oxford University Press, 1991, pp.401- 406. 24. On the conjectures of Mordell and Lang in positive characteristic. Inventiones Math. 104(1991), 643-646. 25. (with J. Silverman) Multiple Weierstrass Points. Compositio Math. 79(1991), 123-134. 26. (with J. Hirschfeld, L. Storme and J. Thas) A characterization of Hermitian curves. J. Geometry 41(1991), 72-78. 27. (with A. Garcia) for projective curves. Bol. Soc. Brasil. Mat. 21(1991), 159-175. 28. (with D. Abramovich) Toward a proof of the Mordell-Lang conjecture in positive characteristic, Intern. Math. Research Notices, No.5(1992), 103-115. 29. (with R. Coleman) Companion forms and Kodaira-Spencer Theory, Inventiones Math., 110 (1992), 263-281. 30. (with J. Hirschfeld) -arcs of order on cubic curves, in “Finite Geometry and combinatorics,” F. de Clerck et al. eds., LMS Lecture Notes 191, Cambridge Univ. Press, 1993, 177-185. 31. Appendix to “Behaviour of function field Gauss sums at infinity” by D. S. Thakur, Bull. London Math. Soc., 25(1993), 425-426. 32. (with A. Buium) Integral points of abelian varieties over function fields of characteristic zero, Math. Annalen., 297(1993), 303-307. 33. Ramified covers of abelian varieties over function fields, Math. Research Letters, 1 (1994), 465-467. 34. Siegel’s theorem for complex function fields, Proc. Amer. Math. Soc., 121(1994), 1307-1308. 35. (with A. Buium) Reduction of the Manin map modulo p, J. Reine Angew. Math., 460 (1995), 117-126. Jos´eFelipe Voloch Page 4

36. Diophantine approximation in characteristic p, Monatshefte f¨urMathematik, 119 (1995), 321- 325. 37. Diophantine approximation on Abelian Varieties in characteristic p, American Journal of Math., 117 (1995), 1089-1095. 38. (with D. Abramovich) Lang’s conjecture, fibered powers and uniformity, New York Journal of Math., 2 (1996) 20-34. 39. Transcendence of elliptic modular functions in characteristic p, J. Number Theory, 58 (1996) 55-59. 40. (with J. Tate) Linear forms in p-adic roots of unity, Intern. Math. Research Notices, 12 (1996) 589-601. 41. (with A. Buium) Lang’s conjecture in characteristic p: an explicit bound, Compositio Math., 103 (1996) 1-6. 42. Integrality of torsion points on abelian varieties over p-adic fields, Math. Research Letters, 3 (1996) 787-791. 43. An analogue of the Weierstrass ζ-function in characteristic p, Acta Arithmetica, LXXIX (1997) 1-6. 44. in characteristic p: a survey, , F. Catanese, ed., Symposia Mathematica XXXVII, Cambridge Univ. Press, 1997, pp. 260-278. 45. Distance functions on varieties over non-archimedean local fields, Rocky Mountain Journal of Math., 27 (1997) 635-641. 46. Differential operators and interpolation series in power series fields, J. Number Theory, 71 (1998) 106-108. 47. Periods of ordinary abelian varieties in characteristic p, Bol. Soc. Brasil. Mat., 29 (1998) 295-300. 48. The equation ax + by = 1 in characteristic p, J. Number Theory, 73 (1998) 195-200. 49. (with J. Walker) Lee weights of Z/4Z-codes from elliptic curves in Codes, Curves, and Signals: Common Threads in Communications, A. Vardy, ed., Kluwer, Boston 1998, pp. 53-62. 50. (with F. Rodr´ıguezVillegas) On certain plane curves with many integral points, Experimental Math., 8 (1999) 57-62. 51. (with T. Scanlon) Difference algebraic subgroups of commutative algebraic groups over finite fields, Manuscripta Math., 99 (1999) 329-339. 52. (with J. Walker) Codes over rings from curves of higher genus, IEEE Transactions in , 45 (1999) 1768-1776. 53. On the p-adic Waring’s problem, Acta Arithmetica, 90 (1999) 91-95. 54. Plane curves and p-adic roots of unity, Bull. Australian Math. Soc., 60 (1999) 479-482. 55. Elliptic Wieferich primes, J. Number Theory, 81 (2000) 205-209. 56. On a question of Buium, Canadian Math. Bull., 43 (2000) 236-238. 57. Chebyshev’s method for number fields, J. de Th´eoriedes Nombres de Bordeaux, 12 (2000) 81-85. 58. Jacobians of curves over finite fields, Rocky Mountain Journal of Math., 30 (2000) 755-759. 59. (with J. Walker) Euclidean weights of codes from elliptic curves over rings, Trans. Amer. Math. Soc., 352 (2000), 5063-5076. 60. (with J. Vaaler) The least nonsplit prime in Galois extensions of Q, J. Number Theory, 85 (2000), 320-335. 61. A note on the arithmetic of differential equations, Indagationes Mathematicae, 11 (2000) 617- 621. 62. (with M. Kim and D. Thakur) Diophantine Approximation and Deformations, Bull. Soc. Math. France, 128 (2000) 585-598. 63. On the duals of binary BCH codes, IEEE Transactions in Information Theory, 47 (2001) 2050- 2051. Jos´eFelipe Voloch Page 5

64. (with F. Rodriguez Villegas and D. Zagier) Constructions of plane curves with many points, Acta Arithmetica, 99 (2001) 85-96. 65. (with F. Rodriguez Villegas and L. Sadun) Blet: a mathematical puzzle, Amer. Math. Monthly, 109 (2002) 729-740. 66. (with J. Walker) Homogeneous Weights and Exponential Sums, Finite Fields and Appl., 9 (2003) 310–321. 67. Surfaces in P3 over finite fields, in Topics in Algebraic and Noncommutative Geometry: Pro- ceedings in Memory of Ruth Michler, C. Melles et al. eds., Contemporary Math. 324 (2003) 219–226. 68. (with B. Poonen) Random Diophantine Equations, in Arithmetic of higher dimensional algebraic varieties, B. Poonen and Y. Tschinkel, eds. Progress in Mathematics 226, Birkauser, Boston 2004, pp. 175–184. 69. (with T. Helleseth) Double Circulant Quadratic Residue Codes, IEEE Transactions on Infor- mation Theory, 50 (2004) 2154–2155. 70. On some subgroups of the multiplicative group of finite rings, J. de Th´eoriedes Nombres de Bordeaux, 16 (2004) 233–239. 71. (with M. L. Carlin) Plane curves with many points over finite fields, Rocky Mountain Journal of Math., 34 (2004), 1255–1259. 72. A note on (k,n)-arcs. Proceedings of the Irsee conference on Finite Geometry, Discrete Mathe- matics 294 (2005) 223-224. 73. (with G. McGuire) Weights in codes and genus 2 curves. Proc. Amer. Math. Soc. 133 (2005), 2429–2437. 74. (with P. Barreto) Efficient computation of roots in finite fields, Designs, Codes and Cryptogra- phy 39 (2006), 275–280. 75. (with C. Hall) Towards Lang-Trotter for Elliptic Curves over Function Fields. Pure and Quarterly 2 (2006) 163–178. 76. Computing the minimal distance of cyclic codes. Computational and Applied Mathematics 24 (2005) 393–398. 77. (with I. Shparlinski) Visible Points on Curves over Finite Fields. Bull. Polish Acad. Sci. Math. 55 (2007), 193-199 78. On the order of points on curves over finite fields, , 7 (2007) A49. 79. Symmetric cryptography and algebraic curves. In J. Hirschfeld, J. Chaumine, and R. Rolland, eds., Algebraic geometry and its applications (Proc. of SAGA), Number Theory and Its Ap- plications, Vol. 5, 135–141. World Scientific, 2008. 80. (with I. Shparlinski) Average distribution of prime ideals in families of number fields, Bol. Soc. Brasil. Mat., 39 (2008) 417–425. 81. (with J. Silverman) A Local-Global Criterion for Dynamics on P1, Acta Arith. 137 (2009), 285–294. 82. (with P. Ivanov) Breaking the Akiyama-Goto cryptosystem, Proceedings of AGCT 11, G. Lachaud, C. Ritzenthaler, M. Tsfasman, eds., Contemporary Mathematics 487 (2009) 113- 118. 83. (with B. Poonen) The Brauer-Manin obstruction for subvarieties of abelian varieties over func- tion fields, Annals of Math., 171 (2010), 511–532. 84. (with M. Zarzar) Algebraic Geometric Codes on Surfaces, Proceedings of AGTC 10, S´eminaires et Congr`esSMF 21 (2009) 211–216. 85. (with R. R. Farashahi and I. Shparlinski) On Hashing into Elliptic Curves, Journal of Mathe- matical Cryptology, 3 (2009) 353–360. 86. Conics over function fields and the Artin-Tate conjecture, Houston J. Mathematics, 36 (2010) 675–680. Jos´eFelipe Voloch Page 6

87. (with O. Ahmadi and I. Shparlinski) Multiplicative Order of Gauss Periods, International Journal of Number Theory, 6 (2010) 877–882. 88. Elements of high order on finite fields from elliptic curves, Bull. of the Australian Math. Soc., 81 (2010) 425–429. Articles in Press 89. (with D. Harari) The Brauer-Manin obstruction for integral points on curves, Math. Proc. Cam. Phil. Soc, to appear. 90. Special divisors of large on curves with many points over finite fields, Portugaliae Mathematica, to appear.