School of Mathematics and Statistics,

University of Canterbury,

Private Bag 4800, Christchurch 8140, New Zealand

felipe.voloch@canterbury.ac.nz

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

- Associate Member of The Brazilian Academy of Sciences ( Biographical info there).
- Alfred P. Sloan Fellow, 93-95.

- Professor, School of Mathematics and Statistics, University of Canterbury, 2016-present.
- Visiting Researcher, IMPA, Rio de Janeiro, Brazil, May-Dec 2011.
- Professor, Mathematics Department, University of Texas at Austin, 2000-2017.
- Research Professor, Mathematical Sciences Research Institute, Jan.-Jun. 1998.
- Associate Professor, Mathematics Department, University of Texas at Austin, 1995-2000
- Assistant Professor, Mathematics Department, University of Texas at Austin, 1992-1995
- Visiting Scholar, Mathematics Department, University of California, Berkeley, 1991-1992
- Associate Professor, IMPA, Rio de Janeiro, Brazil, 1991-1992
- Assistant Professor, IMPA, Rio de Janeiro, Brazil, 1985-1991

- Amilcar Pacheco, Ph.D. 1989.
- Jorge Oswaldo Gomes Aarão, M.Sc., 1989.
- Antonios Broumas, Ph.D. 1995.
- Tae Wan Park, M.Sc. 1996.
- Cong Kang, Ph.D. 1999.
- Sangtae Jeong, Ph.D. 1999.
- Luis Renato Abib Finotti. Ph.D. 2001.
- Ana R. B. Neira Ph.D. 2002
- Aby Bentata M.Sc. 2004
- Francisco Portillo Ph.D. 2004
- Marcos Zarzar Ph.D. 2006
- Laura Hitt, Ph.D. 2007.
- Brendan Younger, M.Sc., 2007.
- Rohit Ghosh, Ph.D. 2007.
- Petar Ivanov,M.Sc., 2008.
- Herivelto Borges Filho, Ph.D. 2009.
- Pippa Charters, Ph.D. 2009.
- Ricardo Conceição, Ph.D. 2009.
- James Jones, M.Sc. 2010.
- Chia-Liang Sun, Ph.D. 2011.
- Jennifer S. Berg, Ph.D. 2016.
- Alessandro R. de Macedo, Ph.D. 2017.

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- (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
- (with D. Koutrofiotis) Saddle surfaces admitting local support planes. J. Reine Angew. Math. 385(1985), 1-5. MR 86m 53004
- Diagonal equations over function fields. Bol. Soc. Brasil. Mat. 16(1985), 29-39. MR 87g 11157
- (with K.-O. Stohr) Weierstrass points and curves over finite fields. Proc. London Math. Soc. (30) 52(1986), 1-19. MR 87b 14010
- On the completeness of certain plane arcs. European J. Combinatorics 8 (1987), 453-456. MR 89e 51011
- Arcs in projective planes over prime fields. J. Geometry 38 (1990) 198-200. MR 91f 51020
- (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
- Diophantine approximation in positive characteristic. Periodica Math. Hungarica 19(1988), 217-225. MR 89h 11045
- A note on algebraic curves in characteristic two. Comm. Algebra 16(4)(1988), 869-875. MR 89b 14044
- A note on elliptic curves over finite fields. Bull. Soc. Math. France 116(1988), 455-458. MR 90f 14012
- (with J. Hirschfeld) The characterization of elliptic curves over finite fields. J. Australian Math. Soc. Ser. A 45(1988), 275-286. MR 89g 14011
- (with A. Garcia) Wronskians and linear independence in prime characteristic. Manuscripta Math. 59(1987), 457-469. MR 88m 12005
- On the number of values taken by a polynomial over a finite field. Acta Arithmetica LII(1989), 197-201. MR 90j 11138
- (with I. Vainsencher) On the Castelnuovo-Severi inequality. J. Reine Angew. Math. 390(1988), 114-116. MR 90e 14006
- (with A. Garcia) Fermat curves over finite fields. J. Number Theory 30(1988), 345-356. MR 90a 14027
- (with A. Hefez) Frobenius non-classical curves. Arch. Math. (Basel) 54(1990), 263-273. MR 91e 14018
- On the geometry of space curves. Proc. of the 10th School of Algebra, IMPA, Rio de Janeiro, 1990, pp.121-122.
- On the completeness of certain plane arcs II. European J. Combinatorics 11(1990), 491-496. MR 91i 51017
- Mordell's equation in characteristic three. Bull. Australian Math. Soc. 47 (1990), 149-150. MR 91b 11072
- Explicit p-descent for elliptic curves in characteristic p. Compositio Math. 74(1990), 247-258. MR 91f 11042
- Primitive points on constant elliptic curves over function fields. Bol. Soc. Brasil. Mat. 21(1990), 91-94. MR 93e 11078
- A diophantine problem on algebraic curves over function fields of positive characteristic. Bull. Soc. Math. France, 119(1991), 121-126. MR 92g 11061
- 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
- On the conjectures of Mordell and Lang in positive characteristic. Inventiones Math. 104(1991), 643-646. MR 92d 11067
- (with J. Silverman) Multiple Weierstrass Points. Compositio Math. 79(1991), 123-134. MR 92f 14027
- (with J. Hirschfeld, L. Storme and J. Thas) A characterization of Hermitian curves. J. Geometry 41(1991), 72-78. MR 92d 51005
- (with A. Garcia) Duality for projective curves. Bol. Soc. Brasil. Mat. 21(1991), 159-175. MR 93g 14039
- (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
- (with R. Coleman) Companion forms and Kodaira-Spencer Theory, Inventiones Math., 110(1992), 263-281. MR 93i 11063
- (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
- 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
- (with A. Buium) Integral points of abelian varieties over function fields of characteristic zero, Math. Annalen., 297(1993), 303-307. MR 94i 14029
- Ramified covers of abelian varieties over function fields, Math. Research Letters, 1 (1994), 465-467. MR 95i 11063
- Siegel's theorem for complex function fields, Proc. Amer. Math. Soc., 121(1994), 1307-1308. MR 94j 11052
- (with A. Buium) Reduction of the Manin map modulo p, J. Reine Angew. Math., 460 (1995), 117-126. MR 96a 14052
- Diophantine approximation in characteristic p, Monatshefte fur Mathematik, 119 (1995), 321-325. MR 96b 11099
- Diophantine approximation on Abelian Varieties in characteristic p, American Journal of Math., 117 (1995), 1089-1095. MR 96i 11061
- (with D. Abramovich) Lang's conjecture, fibered powers and uniformity, New York Journal of Math., 2 (1996) 20-34. MR 97e 14031
- Transcendence of elliptic modular functions in characteristic p, J. Number Theory, 58 (1996) 55-59. MR 98a 11099
- (with J. Tate) Linear forms in p-adic roots of unity, Intern. Math. Research Notices, 12 (1996) 589-601. MR 97h 11065
- (with A. Buium) Lang's conjecture in characteristic p: an explicit bound, Compositio Math., 103 (1996) 1-6. MR 98a 14038
- 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
- An analogue of the Weierstrass zeta-function in characteristic p, Acta Arithmetica, LXXIX (1997) 1-6. MR 98c:11052
- Integrality of torsion points on abelian varieties over p-adic fields, Math. Research Letters, 3 (1996) 787-791. MR 98a 14036
- Distance functions on varieties over non-archimedean local fields, Rocky Mountain Journal of Math., 27 (1997) 635-641. MR 98g 14021
- Periods of ordinary abelian varieties in characteristic p, Bol. Soc. Brasil. Mat., 29 (1998) 295-300. MR 99j 14046
- (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.
- Differential operators and interpolation series in power series fields, J. Number Theory, 71 (1998) 106-108. MR 99j 13019
- The equation ax+by=1 in characteristic p, J. Number Theory, 73 (1998) 195-200. MR 2000b 11029
- (with F. Rodríguez Villegas) On certain plane curves with many integral points, Experimental Math., 8 (1999) 57-62. MR 2000b 14025
- On a question of Buium, Canadian Math. Bull., 43 (2000) 236-238.
- (with T. Scanlon) Difference algebraic subgroups of commutative algebraic groups over finite fields, Manuscripta Math., 99 (1999) 329-339.
- On the p-adic Waring's problem, Acta Arithmetica, 90 (1999) 91-95.
- (with J. Walker) Codes over rings from curves of higher genus, IEEE Transactions in Information Theory, 45 (1999) 1768-1776.
- Jacobians of curves over finite fields, Rocky Mountain Journal of Math., 30 (2000) 755-759.
- Plane curves and p-adic roots of unity, Bull. Australian Math. Soc., 60 (1999) 479-482.
- (with J. Walker) Euclidean weights of codes from elliptic curves over rings, Trans. Amer. Math. Soc., 352 (2000), 5063-5076.
- Elliptic Wieferich primes, J. Number Theory, 81 (2000) 205-209.
- (with
J. Vaaler)
The least nonsplit prime in Galois extensions of
**Q**, J. Number Theory, 85 (2000), 320-335. - Chebyshev's method for number fields, J. de Théorie des Nombres de Bordeaux, 12 (2000) 81-85.
- (with M. Kim and D. Thakur) Diophantine Approximation and Deformations, Bull. Soc. Math. France, 128 (2000) 585-598.
- (with F. Rodríguez Villegas and D. Zagier) Constructions of plane curves with many points, Acta Arithmetica, 99 (2001) 85-96.
- A note on the arithmetic of differential equations, Indagationes Mathematicae, 11 (2000) 617-621.
- On the duals of binary BCH codes, IEEE Transactions in Information Theory, 47 (2001) 2050-2051.
- (with F. Rodríguez Villegas and L. Sadun) Blet: a mathematical puzzle, Amer. Math. Monthly, 109 (2002) 729-740.
- Surfaces in
**P**^{3}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. - (with M. L. Carlin) Plane curves with many points over finite fields, Rocky Mountain Journal of Math., 34 (2004), 1255-1259.
- (with J. Walker) Homogeneous Weights and Exponential Sums, Finite Fields and Appl., 9 (2003) 310-321.
- On some subgroups of the multiplicative group of finite rings, J. de Théorie des Nombres de Bordeaux, 16 (2004) 233-239.
- (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.
- A note on (k,n)-arcs. Proceedings of the Irsee conference on Finite Geometry, Discrete Mathematics 294 (2005) 223-224.
- (with G. McGuire) Weights in codes and genus 2 curves. Proc. Amer. Math. Soc., 133 (2005), 2429-2437.
- (with T. Helleseth) Double Circulant Quadratic Residue Codes IEEE Transactions on Information Theory, 50 (2004) 2154-2155.
- Computing the minimal distance of cyclic codes. Computational and Applied Mathematics 24 (2005) 393-398.
- (with C. Hall) Towards Lang-Trotter for Elliptic Curves over Function Fields. Pure and Applied Mathematics Quarterly 2 (2006) 163-178.
- (with P. Barreto) Efficient computation of roots in finite fields, Designs, Codes and Cryptography, 39 (2006) 275-280.
- (with M. Zarzar) Algebraic Geometric Codes on Surfaces, Proceedings of AGCT 10, Séminaires et Congrès SMF, 21 (2009) 211--216.
- (with I. Shparlinski) Visible Points on Curves over Finite Fields. Bulletin of the Polish Academy of Sciences, Mathematics,, 55 (2007), 193-199.
- 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.
- On the order of points on curves over finite fields. Integers, 7 (2007) A49.
- (with I. Shparlinski) Average distribution of prime ideals in families of number fields Bol. Soc. Brasil. Mat., 39 (2008) 417-425.
- Conics over function fields and the Artin-Tate conjecture, Houston J. Mathematics,36 (2010) 675-680.
- (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.
- (with
J. Silverman) A Local-Global Criterion for Dynamics on
**P**^{1}, Acta Arith. 137 (2009), 285-294. - (with B. Poonen) The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields, Annals of Math., 171 (2010), 511-532.
- (with O. Ahmadi and I. Shparlinski) Multiplicative Order of Gauss Periods, International Journal of Number Theory, 6 (2010) 877-882.
- Elements of high order on finite fields from elliptic curves, Bull. of the Australian Math. Soc., 81 (2010) 425-429.
- (with R. R. Farashahi and I. Shparlinski) On Hashing into Elliptic Curves, Journal of Mathematical Cryptology, 3 (2009) 353-360.
- (with David Harari) The Brauer-Manin obstruction for integral points on curves, Math. Proc. Cam. Phil. Soc, 149 (2010), 413-421.
- Special divisors of large dimension on curves with many points over finite fields, Portugaliae Mathematica, 68 (2011) 103-107.
- (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
- (with D. Helm) Finite descent obstruction on curves and modularity, BLMS, 43 (2011) 805-810.
- Finite descent obstruction for curves over function fields, Bol. Soc. Brasil. Mat., 43 (2012) 1-6.
- (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.
- (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.
- (with David Harari) Descent obstructions and Brauer-Manin obstruction in positive characteristic Journal de l'Institut de Mathématiques de Jussieu, 12 (2013) 545-551.
- Elements of high order. Chapter in Handbook of Finite Fields, G. Mullen and D. Panario, eds. CRC Press, 2013, pp 98-99.
- Differential descent obstructions over function fields, Proc. Amer. Math. Soc., 142 (2014) 3421-3424.
- (with M. Zieve) Rational points on some Fermat curves and surfaces over finite fields, International Journal of Number Theory, 10 (2014), 319-325.
- (with I. Shparlinski) Generators of elliptic curves over finite fields, Bull. Inst. Math. Acad. Sinica, 9 (2014), 657-670.
- Planar surfaces in positive characteristic, São Paulo J. of Math. Sciences, 10 (2016) 1-8.
- Generators of finite fields with powers of trace zero and cyclotomic function fields, Portugaliae Mathematica, 73 (2016) 65-70.
- (with E. Amerik, P. Kurlberg, K. Nguyen, A. Towsley, B. Viray) Evidence for the dynamical Brauer-Manin criterion, Experimental Mathematics, 25 (2016) 54-65.
- (with S. Patrikis and Y. Zarhin) Anabelian geometry and descent obstructions on moduli spaces, Algebra and Number Theory, 10 (2016), 1191–1219.
- (with B. Creutz) Local-global principles for Weil-Châtelet divisibility in positive characteristic, Math. Proc. Cam. Phil. Soc., 163 (2017) 357-367.
- (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.
- (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.
- (with A. Sutherland), Maps between curves and arithmetic obstructions, Proceedings of AGCT 16, Arithmetic geometry: computation and applications, Contemp. Math., 722 (2019) 167–175.
- (with B. Creutz and B. Viray) The d-primary Brauer-Manin obstruction for curves, Research in Number Theory, (2018) 4: 26.
- (with Yves Aubry and Fabien Herbaut), Maximal differential uniformity polynomials, Acta Arithmetica, 188.4 (2019) 345-366.
- (with I. Shparlinski) Binomial exponential sums, Annali della Scuola Normale Superiore di Pisa, Vol. XXI (2020), 931-941.
- (with I. Shparlinski) Value sets of sparse polynomials, Canadian Math. Bull., 63 (2020) 187-196.
- (with B. Creutz) Tate-Shafarevich groups of constant elliptic curves and isogeny volcanos, Contemp. Math., to appear.
- (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).
- (with John Sheekey and Geertrui Van de Voorde) On the product of elements with prescribed trace, J. Australian Math. Soc., to appear.
- Commitment Schemes and Diophantine Equations, Proceedings of ANTS XIV, (S. D. Galbraith, Ed.) Open Book Series 4 (2020) 1-5.
- (with J. Booher) Recovering algebraic curves from L-functions of Hilbert class fields, Research in Number Theory 6, 43 (2020).
- (with B. Creutz) The Brauer-Manin obstruction for constant curves over global function fields, Annales de l'Institut Fourier, to appear.