Alina Ostafe

Address:

School of Mathematics and Statistics
The University of New South Wales (UNSW)
Sydney NSW 2052
Australia

Office: 5104, Red Centre

Email: alina.ostafe@unsw.edu.au

Education

Employment

Research Interests

Curriculum Vitae

Grants and Fellowships

Australian Research Council Grants

Other Grants

Editorial Duties

Service to the Australian Mathematical Community

I am currently serving as the Vice-President of the Australian Mathematical Society.

We welcome new members, please find more information on how to join AustMS following the link. We also welcome any information about mathematical events, recent news, job opportunities, etc, that you may want to promote to AustMS members and other mathematically inclined followers. Please send information on upcoming events and opportunities to news@austms.org.au. You can also find/follow AustMS on the LinkedIn page.

Seminar Organisation

Conference Organisation

Preprints

  1. A. Ostafe and I. E. Shparlinski, Counting Irreducible polynomials with coefficients from thin subgroup, Preprint, 2026.
  2. A. Ostafe and I. E. Shparlinski, Counting integer matrices with square-free determinants, Preprint, 2025.
  3. A. Ostafe and I. Shparlinski, On the frequency of primes preserving dynamical irreducibility of polynomials, Preprint, 2024.
  4. P. Habegger, A. Ostafe and I. Shparlinski, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices, Preprint, 2024.

Publications

  1. A. Ostafe and I. Shparlinski, On the sparsity of integer matrices with a given discriminant, SIAM J. Discrete Math., (In press).
  2. A. Ostafe, C. Pomerance and I. E. Shparlinski, Counting solvable $\mathcal S$-unit equations and linear recurrence sequences with zeros, Proc. Amer. Math. Soc. (In press).
  3. A. Manning, A. Ostafe and I. Shparlinski, Counting matrices over finite rank multiplicative groups, Pacific J. Math., 2026, v. 340, 115-138.
  4. P. Kurlberg, A. Ostafe, Z. Rudnick and I. Shparlinski, On quantum ergodicity for higher dimensional cat maps, Comm. Math. Phys. 2025, v. 406, 174.
  5. A. Berczes, L. Hajdu, A. Ostafe, I. E. Shparlinski, Multiplicative dependence in linear recurrence sequences, Canadian Math. Bull., 2025, v. 68, 1278--1288.
  6. A. Mohammadi, A. Ostafe and I. Shparlinski, On some matrix counting problems, J. London Math. Soc. (In press).
  7. M. Afifurrahman, V. Kuperberg, A. Ostafe and I. Shparlinski, Statistics of ranks, determinants and characteristic polynomials of rational matrices, Forum Math. 2025, v. 37, 1259-1289.
  8. A. Berczes, Y. Bugeaud, K. Gyory, J. Mello, A. Ostafe and M. Sha, Multiplicative dependence of rational values modulo approximate finitely generated groups, Math. Proc. Cambr. Phil. Soc. 2024, v. 177, 149-165.
  9. A. Berczes, Y. Bugeaud, K. Gyory, J. Mello, A. Ostafe and M. Sha, Explicit bounds for the solutions of superelliptic equations over number fields, Forum Math. 2025, v. 37, 135-158.
  10. A. Ferraguti, A. Ostafe and U. Zannier, Cyclotomic and abelian points in backward orbits of rational functions, Adv. Math. 2024, v. 38, 109463
  11. K. Bulinski, A. Ostafe and I. Shparlinski, Counting embeddings of free groups into $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (In press).
  12. A. Ostafe, I. Shparlinski and F. Voloch, Weil sums over small subgroups, Math. Proc. Camb. Phil. Soc. 2024, v. 176, 39-53.
  13. A. Ostafe, I. Shparlinski and F. Voloch, Equations and character sums with matrix powers, Kloosterman sums over small subgroups and quantum ergodicity, Int. Math. Res. Not. 2023, v. 16, 14196-14238.
  14. A. Ostafe, On a Problem of Lang for Matrix Polynomials, Bull. London Math. Soc., 2022, v. 54, 1552-1567. [ Erratum]
  15. R. Dietmann, A. Ostafe and I. Shparlinski, Discriminants of fields generated by polynomials of given height, Israel J. Math. (In press).
  16. D. Ghioca, A. Ostafe, S. Saleh and I. Shparlinski, On sparsity of representations of polynomials as linear combinations of exponential functions, J. London Math. Soc., 2022, v. 105, 2076-2103.
  17. F. Barroero, L. Capuano, L. Merai, A. Ostafe and M. Sha, Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes, Int. Math. Res. Not., 2022, v. 20, 16094-16137.
  18. A. Ostafe, L. Pottmeyer and I. Shparlinski, Perfect powers in value sets and orbits of polynomials, New York J. Math., 2021, v. 27, 903-917.
  19. D. Ghioca, A. Ostafe, S. Saleh and I. Shparlinski, A sparsity result for the Dynamical Mordell-Lang Conjecture in positive characteristic, Bull. Aust. Math. Soc., 2021, v. 104, 381-390
  20. A. Ostafe and I. Shparlinski, On the Skolem problem and some related questions for parametric families of linear recurrence sequences, Canadian J. Math., 2022, v. 74, 773-792.
  21. L. Merai, A. Ostafe and I. Shparlinski, Dynamical irreducibility of polynomials in reduction modulo primes, Mathematische Zeitschrift, 2021, v. 298, 1187-1199.
  22. A. Berczes, A. Ostafe, I. Shparlinski and J. H. Silverman, Multiplicative dependence among iterated values of rational functions modulo finitely generated groups, Int. Math. Res. Not., 2021, v. 12, 9045-9082.
  23. A. Ostafe and M. Young, On algebraic integers of bounded house and preperiodicity in polynomial semigroup dynamics, Trans. Amer. Math. Soc., 2020, v. 373, 2191-2206.
  24. A. Ostafe, M. Sha, I. Shparlinski and U. Zannier, On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem, Michigan Math. J., 2019, v. 68, 385-407.
  25. C. D'Andrea, A. Ostafe, M. Sombra and I. Shparlinski, Modular reduction of systems of polynomial equations and algebraic dynamical systems, Trans. Amer. Math. Soc., 2019, v. 371, 1169-1198.
  26. A. Ostafe, Polynomial values in affine subspaces of finite fields, Journal d'Analyse Mathematique 2019, v. 138, 49-81.
  27. A. Ostafe, M. Sha, I. Shparlinski and U. Zannier, On abelian multiplicatively dependent points on a curve in a toru, Quat. J. Math, 2018, v. 69, 391-401.
  28. C. D'Andrea, M.-C. Chang, A. Ostafe, M. Sombra and I. Shparlinski, Orbits of polynomial dynamical systems modulo primes, Proc. Amer. Math. Soc., 2018, v. 146, 2015-2025.
  29. D. Gomez-Perez, A. Ostafe and M. Sha, The arithmetic of consecutive polynomial sequences over finite field, Finite Fields and Their Appl., 2018, v. 50, 35-65.
  30. A. Ostafe, On roots of unity in orbits of rational functions, Proc. Amer. Math. Soc., 2017, v. 145, 1927-1936.
  31. A. Ostafe and I. Shparlinski, Orbits of Algebraic Dynamical Systems in Subgroups and Subfields, Number Theory - Diophantine problems, uniform distribution and applications,
    Festschrift in Honour of Robert F. Tichy's 60th Birthday, Springer, 2017, 347-368.
  32. A. Ostafe, On some extensions of the Ailon-Rudnick theorem, Monatshefte fur Mathematik, 2016, v. 181, 451-471.
  33. D. Gomez-Perez, J. Gutierrez and A. Ostafe, Common composites of triangular polynomial systems and hash functions, J. Symb. Comp., 2016, v. 72, 182-195.
  34. A. Ostafe and M. Sha, On the quantitative dynamical Mordell-Lang conjecture, J. Number Theory 2015, v. 156, 161-182. (Corrigendum, J. Number Theory, 2016, v. 164, 433-437)
  35. A. Ostafe and M. Sha, Counting dynamical systems over finite fields, Dynamics and Numbers 2014, Contemp. Math., 2016, v. 669, 187-203.
  36. D. Gomez-Perez, A. Ostafe and A. Topuzoglu, On the Carlitz rank of permutations of $\F_p$ and pseudorandom sequences, J. Complexity, 2014, v. 30, 279-289.
  37. D. Gomez, A. Ostafe and I. Shparlinski, On irreducible divisors of iterated polynomials, Revista Matematica Iberoamericana, 2014, 1123-1134.
  38. A. P. Nicolas, A. Ostafe, D. G. Perez and D. Sadornil, Stable polynomials over finite fields, Revista Matematica Iberoamericana, 2014, v. 30, 523-535.
  39. D. Gomez, A. Ostafe and I. Shparlinski, Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators, Math. Comp., 2014, v. 83, 1535-1550.
  40. A. Ostafe, Iterations of rational functions: Some algebraic and arithmetic aspects, Finite Fields and Their Applications. Character Sums and Polynomials, De Gruyter, 2013, 19-232.
  41. A. Ostafe and A. Winterhof, Some applications of character sums, Handbook of Finite Fields, CRC Press, Eds. G. Mullen and D. Panario, 2013, 170--185.
  42. A. Ostafe, Pseudorandom vector sequences of maximal period generated by polynomial dynamical systems, Designs, Codes and Cryptography, 2012, v. 63, 59-72.
  43. J. Cilleruelo, M. Z. Garaev, A. Ostafe and I. Shparlinski, On the concentration of points of polynomial maps and applications, Mathematische Zeitschrift, 2012, v. 272, 825-837.
  44. A. Ostafe and I. Shparlinski, On the power generator and its multivariate analogue, J. Complexity, 2012, v. 28, 238-249.
  45. O. Ahmadi, F. Luca, A. Ostafe and I. Shparlinski, On stable quadratic polynomials, Glasgow Math. J., 2012, v. 54, 359-369.
  46. A. Ostafe and I. Shparlinski, Exponential Sums over Points of Elliptic curves with Reciprocals of Primes, Mathematika, 2012, v. 58, 21-33.
  47. A. Ostafe and I. Shparlinski, Multiplicative Character Sums and Products of Sparse Integers in Residue Classes, Period. Math. Hungarica, 2012, v. 64, 247-255.
  48. A. Ostafe and I. Shparlinski, Degree growth, linear independence and periods of a class of rational dynamical systems, Arithmetic, Geometry, Cryptography and Coding Theory 2010,
    Contemp. Math., 2012, v. 574, 131-143.
  49. A. Ostafe, D. Thomson and A. Winterhof, On the Waring problem with multivariate Dickson polynomials, Finite fields and applications, Contemp. Math., 2012, v. 579, 153-161.
  50. A. Ostafe and I. Shparlinski, On the Waring problem with Dickson polynomials in finite fields, Proc. Amer. Math. Soc., 2011, v.139, 3815-3820.
  51. S. R. Blackburn, A. Ostafe and I. Shparlinski, On the distribution of the subset sum pseudorandom number generator on elliptic curves, Unif. Distrib. Theory, 2011, v. 6, 127-142.
  52. A. Ostafe, I. Shparlinski and A. Winterhof, Multiplicative character sums of a class of nonlinear recurrence vector sequences, Intern. J. Number Theory, 2011, v.7, 1557-1571.
  53. A. Ostafe and I. Shparlinski, Twisted exponential sums over points of elliptic curves, Acta Arith., 2011, v. 148, 77-92.
  54. A. Ostafe and I. E. Shparlinski, Pseudorandomness and dynamics of Fermat quotients, SIAM J. Discr. Math., 2011, v. 25, 50-71.
  55. A. Ostafe, E. Pelican and I. Shparlinski, On pseudorandom numbers from multivariate polynomial systems, Finite Fields and Their Appl., 2010, v.16, 320-328.
  56. A. Ostafe, I. E. Shparlinski and A. Winterhof, On the generalized joint linear complexity profile of a class of nonlinear pseudorandom multisequences, Adv. in Math. of Communications, 2010, v.4, 369-379.
  57. A. Ostafe and I. Shparlinski, On the length of critical orbits of stable quadratic polynomials, Proc. Amer. Math. Soc., 2010, v. 138, 2653-2656.
  58. A. Ostafe and I. Shparlinski, Pseudorandom numbers and hash functions from iterations of multivariate polynomials, Cryptography and Communications, 2010, v. 2, 49-67.
  59. A. Ostafe, Multivariate permutation polynomial systems and nonlinear pseudorandom number generators, Finite Fields and Their Appl., 2010, 144-154.
  60. Z. Chen, A. Ostafe and A. Winterhof, Structure of pseudorandom numbers derived from Fermat quotients, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2010, 73-85.
  61. A. Ostafe, Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2010, 62-72.
  62. A. Ostafe and I. Shparlinski, On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators, Math. Comp., 2010, v. 79, 501-511.
  63. R. Ferguson, C. Hoffman, F. Luca, A. Ostafe and I. E. Shparlinski, Some additive combinatorics problems in matrix rings, Revista Matematica Complutense, 2010, v.23, 501-513.

Postdocs

PhD Students

Becoming a PhD student: What does it take?

During 2018 - 2021 I organised an annual information session dedicated to students in years 3+, which aims to give some insight into the application process for PhD positions in Australia and overseas.

Teaching (lectures only)