José Felipe Voloch

CURRICULUM VITAE

Address

School of Mathematics and Statistics,
University of Canterbury,
Private Bag 4800, Christchurch 8140, New Zealand

felipe.voloch@canterbury.ac.nz

Education

Ph.D., 1985
University of Cambridge, UK (Advisor: J.W.S. Cassels)

Cert. Advanced studies in Math., 1983
University of Cambridge, UK

M.Sc., 1982
IMPA, Rio de Janeiro, Brazil

Honors and Awards

Work Experience

Graduate Students

Editorial positions

Publications

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  1. (with J. M. Gomes) Une inégalité géometrique concernent les points critiques d'une fonction. C. R. Acad. Sci. Paris 295(1982), 535-537. MR 84e 53051
  2. (with D. Koutrofiotis) Saddle surfaces admitting local support planes. J. Reine Angew. Math. 385(1985), 1-5. MR 86m 53004
  3. Diagonal equations over function fields. Bol. Soc. Brasil. Mat. 16(1985), 29-39. MR 87g 11157
  4. (with K.-O. Stohr) Weierstrass points and curves over finite fields. Proc. London Math. Soc. (30) 52(1986), 1-19. MR 87b 14010
  5. On the completeness of certain plane arcs. European J. Combinatorics 8 (1987), 453-456. MR 89e 51011
  6. Arcs in projective planes over prime fields. J. Geometry 38 (1990) 198-200. MR 91f 51020
  7. (with K. O. Stohr) A formula for the Cartier operator on plane algebraic curves. J. Reine Angew. Math. 377(1987), 49-64. MR 88g 14026
  8. Diophantine approximation in positive characteristic. Periodica Math. Hungarica 19(1988), 217-225. MR 89h 11045
  9. A note on algebraic curves in characteristic two. Comm. Algebra 16(4)(1988), 869-875. MR 89b 14044
  10. A note on elliptic curves over finite fields. Bull. Soc. Math. France 116(1988), 455-458. MR 90f 14012
  11. (with J. Hirschfeld) The characterization of elliptic curves over finite fields. J. Australian Math. Soc. Ser. A 45(1988), 275-286. MR 89g 14011
  12. (with A. Garcia) Wronskians and linear independence in prime characteristic. Manuscripta Math. 59(1987), 457-469. MR 88m 12005
  13. On the number of values taken by a polynomial over a finite field. Acta Arithmetica LII(1989), 197-201. MR 90j 11138
  14. (with I. Vainsencher) On the Castelnuovo-Severi inequality. J. Reine Angew. Math. 390(1988), 114-116. MR 90e 14006
  15. (with A. Garcia) Fermat curves over finite fields. J. Number Theory 30(1988), 345-356. MR 90a 14027
  16. (with A. Hefez) Frobenius non-classical curves. Arch. Math. (Basel) 54(1990), 263-273. MR 91e 14018
  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. MR 91i 51017
  19. Mordell's equation in characteristic three. Bull. Australian Math. Soc. 47 (1990), 149-150. MR 91b 11072
  20. Explicit p-descent for elliptic curves in characteristic p. Compositio Math. 74(1990), 247-258. MR 91f 11042
  21. Primitive points on constant elliptic curves over function fields. Bol. Soc. Brasil. Mat. 21(1990), 91-94. MR 93e 11078
  22. A diophantine problem on algebraic curves over function fields of positive characteristic. Bull. Soc. Math. France, 119(1991), 121-126. MR 92g 11061
  23. Complete arcs in Galois planes of non-square order, in Advances in Finite Geometries and Designs, J. Hirschfeld, D. Hughes and J. Thas, eds., Oxford University Press, 1991, pp.401-406. MR 92m 51025
  24. On the conjectures of Mordell and Lang in positive characteristic. Inventiones Math. 104(1991), 643-646. MR 92d 11067
  25. (with J. Silverman) Multiple Weierstrass Points. Compositio Math. 79(1991), 123-134. MR 92f 14027
  26. (with J. Hirschfeld, L. Storme and J. Thas) A characterization of Hermitian curves. J. Geometry 41(1991), 72-78. MR 92d 51005
  27. (with A. Garcia) Duality for projective curves. Bol. Soc. Brasil. Mat. 21(1991), 159-175. MR 93g 14039
  28. (with D. Abramovich) Toward a proof of the Mordell-Lang conjecture in positive characteristic, Intern. Math. Research Notices, No.5(1992), 103-115. MR 94f 11051
  29. (with R. Coleman) Companion forms and Kodaira-Spencer Theory, Inventiones Math., 110(1992), 263-281. MR 93i 11063
  30. (with J. Hirschfeld) Group-arcs of prime power 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. MR 95b 51011
  31. Appendix to ``Behaviour of function field Gauss sums at infinity'' by D. S. Thakur, Bull. London Math. Soc., 25(1993), 425-426. MR 94h 11104
  32. (with A. Buium) Integral points of abelian varieties over function fields of characteristic zero, Math. Annalen., 297(1993), 303-307. MR 94i 14029
  33. Ramified covers of abelian varieties over function fields, Math. Research Letters, 1 (1994), 465-467. MR 95i 11063
  34. Siegel's theorem for complex function fields, Proc. Amer. Math. Soc., 121(1994), 1307-1308. MR 94j 11052
  35. (with A. Buium) Reduction of the Manin map modulo p, J. Reine Angew. Math., 460 (1995), 117-126. MR 96a 14052
  36. Diophantine approximation in characteristic p, Monatshefte fur Mathematik, 119 (1995), 321-325. MR 96b 11099
  37. Diophantine approximation on Abelian Varieties in characteristic p, American Journal of Math., 117 (1995), 1089-1095. MR 96i 11061
  38. (with D. Abramovich) Lang's conjecture, fibered powers and uniformity, New York Journal of Math., 2 (1996) 20-34. MR 97e 14031
  39. Transcendence of elliptic modular functions in characteristic p, J. Number Theory, 58 (1996) 55-59. MR 98a 11099
  40. (with J. Tate) Linear forms in p-adic roots of unity, Intern. Math. Research Notices, 12 (1996) 589-601. MR 97h 11065
  41. (with A. Buium) Lang's conjecture in characteristic p: an explicit bound, Compositio Math., 103 (1996) 1-6. MR 98a 14038
  42. Diophantine geometry in characteristic p: a survey, Arithmetic Geometry, F. Catanese, ed., Symposia Mathematica XXXVII, Cambridge Univ. Press, 1997, pp. 260-278. MR 99c:11081
  43. An analogue of the Weierstrass zeta-function in characteristic p, Acta Arithmetica, LXXIX (1997) 1-6. MR 98c:11052
  44. Integrality of torsion points on abelian varieties over p-adic fields, Math. Research Letters, 3 (1996) 787-791. MR 98a 14036
  45. Distance functions on varieties over non-archimedean local fields, Rocky Mountain Journal of Math., 27 (1997) 635-641. MR 98g 14021
  46. Periods of ordinary abelian varieties in characteristic p, Bol. Soc. Brasil. Mat., 29 (1998) 295-300. MR 99j 14046
  47. (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.
  48. Differential operators and interpolation series in power series fields, J. Number Theory, 71 (1998) 106-108. MR 99j 13019
  49. The equation ax+by=1 in characteristic p, J. Number Theory, 73 (1998) 195-200. MR 2000b 11029
  50. (with F. Rodríguez Villegas) On certain plane curves with many integral points, Experimental Math., 8 (1999) 57-62. MR 2000b 14025
  51. On a question of Buium, Canadian Math. Bull., 43 (2000) 236-238.
  52. (with T. Scanlon) Difference algebraic subgroups of commutative algebraic groups over finite fields, Manuscripta Math., 99 (1999) 329-339.
  53. On the p-adic Waring's problem, Acta Arithmetica, 90 (1999) 91-95.
  54. (with J. Walker) Codes over rings from curves of higher genus, IEEE Transactions in Information Theory, 45 (1999) 1768-1776.
  55. Jacobians of curves over finite fields, Rocky Mountain Journal of Math., 30 (2000) 755-759.
  56. Plane curves and p-adic roots of unity, Bull. Australian Math. Soc., 60 (1999) 479-482.
  57. (with J. Walker) Euclidean weights of codes from elliptic curves over rings, Trans. Amer. Math. Soc., 352 (2000), 5063-5076.
  58. Elliptic Wieferich primes, J. Number Theory, 81 (2000) 205-209.
  59. (with J. Vaaler) The least nonsplit prime in Galois extensions of Q, J. Number Theory, 85 (2000), 320-335.
  60. Chebyshev's method for number fields, J. de Théorie des Nombres de Bordeaux, 12 (2000) 81-85.
  61. (with M. Kim and D. Thakur) Diophantine Approximation and Deformations, Bull. Soc. Math. France, 128 (2000) 585-598.
  62. (with F. Rodríguez Villegas and D. Zagier) Constructions of plane curves with many points, Acta Arithmetica, 99 (2001) 85-96.
  63. A note on the arithmetic of differential equations, Indagationes Mathematicae, 11 (2000) 617-621.
  64. On the duals of binary BCH codes, IEEE Transactions in Information Theory, 47 (2001) 2050-2051.
  65. (with F. Rodríguez Villegas and L. Sadun) Blet: a mathematical puzzle, Amer. Math. Monthly, 109 (2002) 729-740.
  66. Surfaces in P3 over finite fields, in Topics in Algebraic and Noncommutative Geometry: Proceedings in Memory of Ruth Michler, C. Melles et al. eds., Contemporary Math. 324 (2003) 219-226.
  67. (with M. L. Carlin) Plane curves with many points over finite fields, Rocky Mountain Journal of Math., 34 (2004), 1255-1259.
  68. (with J. Walker) Homogeneous Weights and Exponential Sums, Finite Fields and Appl., 9 (2003) 310-321.
  69. On some subgroups of the multiplicative group of finite rings, J. de Théorie des Nombres de Bordeaux, 16 (2004) 233-239.
  70. (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.
  71. A note on (k,n)-arcs. Proceedings of the Irsee conference on Finite Geometry, Discrete Mathematics 294 (2005) 223-224.
  72. (with G. McGuire) Weights in codes and genus 2 curves. Proc. Amer. Math. Soc., 133 (2005), 2429-2437.
  73. (with T. Helleseth) Double Circulant Quadratic Residue Codes IEEE Transactions on Information Theory, 50 (2004) 2154-2155.
  74. Computing the minimal distance of cyclic codes. Computational and Applied Mathematics 24 (2005) 393-398.
  75. (with C. Hall) Towards Lang-Trotter for Elliptic Curves over Function Fields. Pure and Applied Mathematics Quarterly 2 (2006) 163-178.
  76. (with P. Barreto) Efficient computation of roots in finite fields, Designs, Codes and Cryptography, 39 (2006) 275-280.
  77. (with M. Zarzar) Algebraic Geometric Codes on Surfaces, Proceedings of AGCT 10, Séminaires et Congrès SMF, 21 (2009) 211--216.
  78. (with I. Shparlinski) Visible Points on Curves over Finite Fields. Bulletin of the Polish Academy of Sciences, Mathematics,, 55 (2007), 193-199.
  79. Symmetric Cryptography and Algebraic Curves, in Algebraic geometry and its applications (Proc. of SAGA), J. Hirschfeld, J. Chaumine, and R. Rolland, eds., Number Theory and Its Applications, Vol. 5, 135-141. World Scientific, 2008.
  80. On the order of points on curves over finite fields. Integers, 7 (2007) A49.
  81. (with I. Shparlinski) Average distribution of prime ideals in families of number fields Bol. Soc. Brasil. Mat., 39 (2008) 417-425.
  82. Conics over function fields and the Artin-Tate conjecture, Houston J. Mathematics,36 (2010) 675-680.
  83. (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.
  84. (with J. Silverman) A Local-Global Criterion for Dynamics on P1, Acta Arith. 137 (2009), 285-294.
  85. (with B. Poonen) The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields, Annals of Math., 171 (2010), 511-532.
  86. (with O. Ahmadi and I. Shparlinski) Multiplicative Order of Gauss Periods, International Journal of Number Theory, 6 (2010) 877-882.
  87. Elements of high order on finite fields from elliptic curves, Bull. of the Australian Math. Soc., 81 (2010) 425-429.
  88. (with R. R. Farashahi and I. Shparlinski) On Hashing into Elliptic Curves, Journal of Mathematical Cryptology, 3 (2009) 353-360.
  89. (with David Harari) The Brauer-Manin obstruction for integral points on curves, Math. Proc. Cam. Phil. Soc, 149 (2010), 413-421.
  90. Special divisors of large dimension on curves with many points over finite fields, Portugaliae Mathematica, 68 (2011) 103-107.
  91. (with X. Faber) On the Number of Places of Convergence for Newton's Method over Number Fields, J. de Théorie des Nombres de Bordeaux, 23 (2011), 387-401
  92. (with D. Helm) Finite descent obstruction on curves and modularity, BLMS, 43 (2011) 805-810.
  93. Finite descent obstruction for curves over function fields, Bol. Soc. Brasil. Mat., 43 (2012) 1-6.
  94. (with R. R. Farashahi, Pierre-Alain Fouque, I. Shparlinski, Mehdi Tibouchi) Indifferentiable Deterministic Hashing to Elliptic and Hyperelliptic Curves, Math. Comp. 82 (2013), 491-512.
  95. (with Ricardo Conceição and Douglas Ulmer) Unboundedness of the number of rational points on curves over function fields, New York J.of Math. 18 (2012) 291-293.
  96. (with David Harari) Descent obstructions and Brauer-Manin obstruction in positive characteristic Journal de l'Institut de Mathématiques de Jussieu, 12 (2013) 545-551.
  97. Elements of high order. Chapter in Handbook of Finite Fields, G. Mullen and D. Panario, eds. CRC Press, 2013, pp 98-99.
  98. Differential descent obstructions over function fields, Proc. Amer. Math. Soc., 142 (2014) 3421-3424.
  99. (with M. Zieve) Rational points on some Fermat curves and surfaces over finite fields, International Journal of Number Theory, 10 (2014), 319-325.
  100. (with I. Shparlinski) Generators of elliptic curves over finite fields, Bull. Inst. Math. Acad. Sinica, 9 (2014), 657-670.
  101. Planar surfaces in positive characteristic, São Paulo J. of Math. Sciences, 10 (2016) 1-8.
  102. Generators of finite fields with powers of trace zero and cyclotomic function fields, Portugaliae Mathematica, 73 (2016) 65-70.
  103. (with E. Amerik, P. Kurlberg, K. Nguyen, A. Towsley, B. Viray) Evidence for the dynamical Brauer-Manin criterion, Experimental Mathematics, 25 (2016) 54-65.
  104. (with S. Patrikis and Y. Zarhin) Anabelian geometry and descent obstructions on moduli spaces, Algebra and Number Theory, 10 (2016), 1191–1219.
  105. (with B. Creutz) Local-global principles for Weil-Châtelet divisibility in positive characteristic, Math. Proc. Cam. Phil. Soc., 163 (2017) 357-367.
  106. (with Douglas Ulmer) On the number of rational points on special families of curves over function fields, New Zealand Journal of Mathematics, 47 (2017) 1-7.
  107. (with R. de la Bretèche, M. Sha, I. Shparlinski) The Sato-Tate distribution in thin parametric families of elliptic curves, Math. Zeit., (2018) 290: 831.
  108. (with A. Sutherland), Maps between curves and arithmetic obstructions, Proceedings of AGCT 16, Arithmetic geometry: computation and applications, Contemp. Math., 722 (2019) 167–175.
  109. (with B. Creutz and B. Viray) The d-primary Brauer-Manin obstruction for curves, Research in Number Theory, (2018) 4: 26.
  110. (with Yves Aubry and Fabien Herbaut), Maximal differential uniformity polynomials, Acta Arithmetica, 188.4 (2019) 345-366.
  111. (with I. Shparlinski) Binomial exponential sums, Annali della Scuola Normale Superiore di Pisa, Vol. XXI (2020), 931-941.
  112. (with I. Shparlinski) Value sets of sparse polynomials, Canadian Math. Bull., 63 (2020) 187-196.
  113. (with B. Creutz) Tate-Shafarevich groups of constant elliptic curves and isogeny volcanos, in Abelian Varieties and Number Theory (M. Jarden and T. Shaska, eds.) Contemp. Math. 767 (2021) 41-50.
  114. (with Ricardo Barros) Effect of variation in density on the stability of bilinear shear currents with a free surface, Physics of Fluids, 32, 022102 (2020).
  115. (with John Sheekey and Geertrui Van de Voorde) On the product of elements with prescribed trace, J. Australian Math. Soc., 112 (2022) 264-288.
  116. Commitment Schemes and Diophantine Equations, Proceedings of ANTS XIV, (S. D. Galbraith, Ed.) Open Book Series 4 (2020) 1-5.
  117. (with J. Booher) Recovering algebraic curves from L-functions of Hilbert class fields, Research in Number Theory 6, 43 (2020).
  118. (with B. Creutz) The Brauer-Manin obstruction for constant curves over global function fields, Annales de l'Institut Fourier 72 (2022) 43-58.
  119. (with C. Salgado and A. Várilly-Alvarado) Locally Recoverable Codes on Surfaces, IEEE Transactions on Information Theory, 67 (2021) 5765-5777.
  120. (with J. Booher) Recovering affine curves over finite fields from L-functions, Pacific J. of Math., 314-1 (2021), 1-28.
  121. (with J. Booher, R. Bowden, J. Doliskani, T. B. Fouotsa, S. D. Galbraith, S. Kunzweiler, S.-P. Merz, C. Petit, B. Smith, K. Stange, Y. B. Ti, C. Vincent, C. Weitkämper and L. Zobernig) Failing to hash into supersingular isogeny graphs, Presented at CFAIL 2022. The Computer Journal, to appear.
  122. (with A. Ostafe and I. Shparlinski) Equations and character sums with matrix powers, Kloosterman sums over small subgroups and quantum ergodicity, IMRN, 16 (2023) 14196-14238.
  123. (with J. Berg) Rational points on symmetric squares of constant algebraic curves over function fields, J. de Théorie des Nombres de Bordeaux, 35 (2023) 467-480.
  124. (with A. Ostafe and I. Shparlinski) Weil sums over small subgroups, Math. Proc. Cam. Phil. Soc., 176 (2024) 39-53.
  125. (with B. Creutz) Etale descent obstruction and anabelian geometry of curves over finite fields, Épijournal de Géométrie Algébrique, to appear.