Alina Ostafe

Address:

Office: 4078, Red Centre

Email: alina.ostafe@unsw.edu.au

Telephone: +61 (02)93853976

Education

• 2010: PhD., Institute of Mathematics, University of Zurich, Switzerland
  PhD Thesis: "Polynomial Dynamics and Pseudorandomness"
  Supervisors: Prof. Joachim Rosenthal and Prof. Markus Brodmann
• 2007: MSc., University of Bucharest, Romania
• 2005: Diploma, Advanced Undergraduate Studies in Mathematics, Scoala Normala Superioara Bucharest, Romania

Employment

• July 2018 - : Senior Lecturer, School of Mathematics and Statistics, UNSW Sydney, Australia
• October 2016 - June 2018: Lecturer, School of Mathematics and Statistics, UNSW Sydney, Australia
• October 2013 - September 2016: Postdoc, School of Mathematics and Statistics, UNSW Sydney, Australia
• October 2010 - September 2013: Postdoc, Department of Computing, Macquarie University, Sydney, Australia
• September 2007 - September 2010: Research/Teaching Assistant, Institute of Mathematics, University of Zurich
• September 2005 - August 2007: Research Assistant, Institute of Mathematics "Simion Stoilow" of the Romanian Academy, Bucharest, Romania

Areas of Interest

• Arithmetic dynamical systems
• Polynomials and rational functions over local and global fields
• Finite fields and their applications

Curriculum Vitae

You can find more information in my CV (last updated in May 2019).

Seminar Organisation

• Number Theory Seminar, UNSW Sydney

Conference Organisation

• September 30 - October 3, 2019, Number Theory Down Under 7, UNSW Sydney
  Organizers: A. Ostafe, J. Roberts, I. Shparlinski, L. Zhao
• March 28 - April 2, 2016, Dynamics and Graphs over Finite Fields: Algebraic, Number Theoretic and Algorithmic Aspects, CIRM, Luminy
  Organizers: M.-C. Chang, J. von zur Gathen, A. Ostafe and F. Pappalardi
• February 2 - 6, 2015, Workshop on Algebraic, Number Theoretic and Graph Theoretic Aspects of Dynamical Systems, UNSW Sydney
  Organisers: B. McKay, A. Ostafe, J. Roberts and I. Shparlinski
  
• May 19 - 23, 2014, Polynomials over Finite Fields: Functional and Algebraic Properties, CRM, Barcelona
  Organizers: J. von zur Gathen, J. Gutierrez, A. Ostafe, D. Panario, A. Topuzoglu
• December 9 - 13, 2013, Finite fields and their applications, RICAM, Linz
  Organizers: H. Niederreiter, A. Ostafe, D. Panario and I. Shaprlinski
• May 5 - 10, 2013, The Art of Iterating Rational Functions over Finite Fields, Banff
  Organizers: N. Boston, A. Ostafe, I. Shparlinski, M. Zieve

Publications

1. 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.
2. A. Ostafe and I. E. Shparlinski, On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators, Math. Comp., 2010, v. 79, 501-511.
3. A. Ostafe, Multivariate permutation polynomial systems and nonlinear pseudorandom number generators, Finite Fields and Their Appl., 2010, 144-154.
4. A. Ostafe and I. E. Shparlinski, Pseudorandom numbers and hash functions from iterations of multivariate polynomials, Cryptography and Communications, 2010, v. 2, 49-67.
5. A. Ostafe and I. E. Shparlinski, On the length of critical orbits of stable quadratic polynomials, Proc. Amer. Math. Soc., 2010, v. 138, 2653-2656.
6. 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.
7. A. Ostafe, E. Pelican and I. E. Shparlinski, On pseudorandom numbers from multivariate polynomial systems, Finite Fields and Their Appl., 2010, v.16, 320-328.
8. A. Ostafe and I. E. Shparlinski, Pseudorandomness and dynamics of Fermat quotients, SIAM J. Discr. Math., 2011, v. 25, 50-71.
9. 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.
10. A. Ostafe, Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2010, 62-72.
11. A. Ostafe and I. E. Shparlinski, Twisted exponential sums over points of elliptic curves, Acta Arith., 2011, v. 148, 77-92.
12. A. Ostafe, I. E. Shparlinski and A. Winterhof, Multiplicative character sums of a class of nonlinear recurrence vector sequences, Intern. J. Number Theory, 2011, v.7, 1557-1571.
13. A. Ostafe and I. E. Shparlinski, On the Waring problem with Dickson polynomials in finite fields, Proc. Amer. Math. Soc., 2011, v.139, 3815-3820.
14. S. R. Blackburn, A. Ostafe and I. E. Shparlinski, On the distribution of the subset sum pseudorandom number generator on elliptic curves, Unif. Distrib. Theory, 2011, v. 6, 127-142.
15. A. Ostafe and I. E. Shparlinski, Multiplicative Character Sums and Products of Sparse Integers in Residue Classes, Period. Math. Hungarica, 2012, v. 64, 247-255.
16. A. Ostafe and I. E. Shparlinski, Exponential Sums over Points of Elliptic curves with Reciprocals of Primes, Mathematika, 2012, v. 58, 21-33.
17. A. Ostafe, Pseudorandom vector sequences of maximal period generated by polynomial dynamical systems, Designs, Codes and Cryptography, 2012, v. 63, 59-72.
18. A. Ostafe and I. E. Shparlinski, On the power generator and its multivariate analogue, J. Complexity, 2012, v. 28, 238-249.
19. O. Ahmadi, F. Luca, A. Ostafe and I. E. Shparlinski, On stable quadratic polynomials, Glasgow Math. J., 2012, v. 54, 359-369.
20. J. Cilleruelo, M. Z. Garaev, A. Ostafe and I. E. Shparlinski, On the concentration of points of polynomial maps and applications, Mathematische Zeitschrift, 2012, v. 272, 825-837.
21. A. Ostafe and I. E. 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.
22. 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.
23. 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.
24. 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.
25. A. P. Nicolas, A. Ostafe, D. G. Perez and D. Sadornil, Stable polynomials over finite fields, Revista Matematica Iberoamericana, 2014, v. 30, 523-535.
26. D. Gomez, A. Ostafe and I. E. Shparlinski, On irreducible divisors of iterated polynomials, Revista Matematica Iberoamericana, 2014, 1123-1134.
27. D. Gomez, A. Ostafe and I. E. Shparlinski, Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators, Math. Comp., 2014, v. 83, 1535-1550.
28. 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.
29. D. Gomez-Perez, J. Gutierrez and A. Ostafe, Collisions in compositions of triangular polynomial systems and hash functions', J. Symb. Comp., 2016, v. 72, 182-195.
30. A. Ostafe and M. Sha, Counting dynamical systems over finite fields, Dynamics and Numbers 2014, Contemp. Math., 2016, v. 669, 187-203.
31. 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)
32. A. Ostafe, On some extensions of the Ailon-Rudnick theorem, Monatshefte fur Mathematik, 2016, v. 181, 451-471.
33. A. Ostafe, On roots of unity in orbits of rational functions, Proc. Amer. Math. Soc., 2017, v. 145, 1927-1936.
34. A. Ostafe and I. E. 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.
35. 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.
36. A. Ostafe, Polynomial values in affine subspaces of finite fields, Journal d'Analyse Mathematique (in press).
37. 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.
38. 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.
39. 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.
40. 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. (in press).
41. 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. (in press).

Preprints