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 Nov 2018).

Seminar Organisation

• Number Theory Seminar, UNSW Sydney

Conference Organisation

• 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).

Preprints