Alina Ostafe
Address:
School of Mathematics and Statistics
The University of New South Wales (UNSW)
Sydney NSW 2052
Australia
Office: 5104, Red Centre
Education

2010: PhD., Institute of Mathematics,
University of Zurich,
Switzerland
 2007: MSc.,
University of Bucharest,
Romania
Employment

January 2023  : Associate Professor,
School of Mathematics and Statistics,
UNSW Sydney, Australia

July 2018  December 2022: 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
Research Interests

Number Theory (Diophantine problems; Polynomials and rational functions over local and global fields; Finite fields; Arithmetic statistics of matrices)
 Arithmetic Dynamical Systems
Curriculum Vitae
You can find more information in my CV (last updated on 20 August 2024).
Editorial Duties
Grants
 20232026: Australian Research Council Discovery Project (with I. Shparlinski)
 20202022: Australian Research Council Discovery Project (with I. Shparlinski)
 20182020: Australian Research Council Discovery Project (with J. Roberts and I. Shparlinski)
 2017: UNSW Startup Grant
 2015, 2016, 2017: UNSW Science Faculty Research Grant
 2014: Workshop AMSI/AustMSAMSI/ANZIAM funding (with B. McKay, J. Roberts and I. Shparlinski)
 20132016: UNSW ViceChancellor's Postdoctoral Fellowship
 20122013: Swiss National Science Foundation Grant139679 for Advanced Researchers
 20102012: Swiss National Science Foundation
Grant133399 for Prospective Researchers
Seminar Organisation
Conference Organisation
 9  14 November 2025, Arithmetic Statistics for Algebraic Objects, MFO, Germany
(joint with L. BarySoroker and P. Sarnak)
 23  27 June 2025, Prime Numbers and Arithmetic Randomness, CIRM, Luminy, France
(joint with C Elsholtz, J. Rivat, C. Swaenepoel and T. Stoll)
 28 August  2 September, 2022, Specialisation and Effectiveness in Number Theory, BIRS, Banff, Canada
(joint with C. Stewart, R. Tichy and J. Wang)
 3  5 June 2020, Number Theory Online Conference 2020 (online)
(joint with F. Breuer, M. Coons and T. Morrill)
 30 September  3 October 2019, Number Theory Down Under 7, UNSW Sydney, Australia
(joint with J. Roberts, I. Shparlinski and L. Zhao)
 28 March  2 April 2016, Dynamics and Graphs over Finite Fields: Algebraic, Number Theoretic and Algorithmic Aspects, CIRM, Luminy, France
(joint with M.C. Chang, J. von zur Gathen and F. Pappalardi)
 2  6 February 2015, Workshop on Algebraic, Number Theoretic and Graph Theoretic Aspects of Dynamical Systems, UNSW Sydney, Australia
(joint with B. McKay, J. Roberts and I. Shparlinski)
 19  23 May 2014, Polynomials over Finite Fields: Functional and Algebraic Properties, CRM, Barcelona, Spain
(joint with J. von zur Gathen, J. Gutierrez, D. Panario, A. Topuzoglu)
 9  13 December 2013, Finite fields and their applications, RICAM, Linz, Austria
(joint with H. Niederreiter, D. Panario and I. Shaprlinski)
 5  10 May 2013, The Art of Iterating Rational Functions over Finite Fields, BIRS, Banff, Canada
(joint with N. Boston, I. Shparlinski and M. Zieve)
Preprints
 P. Habegger, A. Ostafe and I. Shparlinski, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices, Preprint, 2024.
 M. Afifurrahman, V. Kuperberg, A. Ostafe and I. Shparlinski, Statistics of ranks, determinants and characteristic polynomials of rational matrices, Preprint, 2023.
 A. Ostafe and I. Shparlinski, On the sparsity of integer matrices with a given discriminant, Preprint, 2023.
 A. Mohammadi, A. Ostafe and I. Shparlinski, On some matrix counting problems, Preprint, 2023.
Publications
 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. (In press).
 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. (In press).
 A. Ferraguti, A. Ostafe and U. Zannier, Cyclotomic and abelian points in backward orbits of rational functions, Adv. Math. (In press).
 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).
 A. Ostafe, I. Shparlinski and F. Voloch, Weil sums over small subgroups, Math. Proc. Camb. Phil. Soc. 2024, v. 176, 3953.
 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, 1419614238.
 A. Ostafe, On a Problem of Lang for Matrix Polynomials, Bull. London Math. Soc., 2022, v. 54, 15521567. [ Erratum]
 R. Dietmann, A. Ostafe and I. Shparlinski, Discriminants of fields generated by
polynomials of given height, Israel J. Math. (In press).
 D. Ghioca, A. Ostafe, S. Saleh and I. E. Shparlinski, On sparsity of representations of polynomials
as linear combinations of exponential functions, J. London Math. Soc., 2022, v. 105, 20762103.
 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, 1609416137.
 A. Ostafe, L. Pottmeyer and I. Shparlinski, Perfect powers in value sets and orbits of polynomials, New York J. Math., 2021, v. 27, 903917.
 D. Ghioca, A. Ostafe, S. Saleh and I. E. Shparlinski, A sparsity result for the Dynamical MordellLang Conjecture in positive
characteristic, Bull. Aust. Math. Soc., 2021, v. 104, 381390
 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, 773792.
 L. Merai, A. Ostafe and I. Shparlinski, Dynamical irreducibility of polynomials in reduction modulo primes, Mathematische Zeitschrift, 2021, v. 298, 11871199.
 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, 90459082.
 A. Ostafe and M. Young, On algebraic integers of bounded house and preperiodicity in polynomial semigroup dynamics, Trans. Amer. Math. Soc., 2020, v. 373, 21912206.
 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, 385407.
 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, 11691198.
 A. Ostafe, Polynomial values in
affine subspaces of finite fields, Journal d'Analyse Mathematique 2019, v. 138, 4981.
 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, 391401.
 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, 20152025.
 D. GomezPerez, A. Ostafe and M. Sha, The arithmetic of consecutive polynomial sequences over finite field, Finite Fields and Their Appl., 2018, v. 50, 3565.
 A. Ostafe, On roots of unity in orbits of rational functions, Proc. Amer. Math. Soc., 2017, v. 145, 19271936.
 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, 347368.
 A. Ostafe, On some extensions of the AilonRudnick theorem, Monatshefte fur Mathematik, 2016, v. 181, 451471.
 D. GomezPerez, J. Gutierrez and A. Ostafe, Common composites of triangular polynomial systems and
hash functions, J. Symb. Comp., 2016, v. 72, 182195.
 A. Ostafe and M. Sha, On the quantitative dynamical MordellLang conjecture, J. Number Theory 2015, v. 156, 161182. (Corrigendum, J. Number Theory, 2016, v. 164, 433437)
 A. Ostafe and M. Sha, Counting dynamical systems over finite fields, Dynamics and Numbers 2014, Contemp. Math., 2016, v. 669, 187203.
 D. GomezPerez, A. Ostafe and A. Topuzoglu, On the Carlitz rank
of permutations of $\F_p$ and pseudorandom sequences,
J. Complexity, 2014, v. 30, 279289.
 D. Gomez, A. Ostafe and I. E. Shparlinski, On irreducible divisors of iterated polynomials,
Revista Matematica Iberoamericana, 2014, 11231134.
 A. P. Nicolas, A. Ostafe, D. G. Perez and D. Sadornil, Stable polynomials over finite fields,
Revista Matematica Iberoamericana, 2014, v. 30, 523535.
 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, 15351550.
 A. Ostafe, Iterations of rational functions: Some algebraic and arithmetic aspects,
Finite Fields and Their Applications. Character Sums and Polynomials, De Gruyter, 2013, 19232.
 A. Ostafe and A. Winterhof, Some applications of character sums,
Handbook of Finite Fields, CRC Press, Eds. G. Mullen and D. Panario, 2013, 170185.
 A. Ostafe,
Pseudorandom vector sequences of maximal period generated by polynomial dynamical systems,
Designs, Codes and Cryptography, 2012, v. 63, 5972.
 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, 825837.
 A. Ostafe and I. E. Shparlinski, On the power generator and its multivariate analogue,
J. Complexity, 2012, v. 28, 238249.
 O. Ahmadi, F. Luca, A. Ostafe and I. E. Shparlinski, On stable quadratic polynomials,
Glasgow Math. J., 2012, v. 54, 359369.
 A. Ostafe and I. E. Shparlinski,
Exponential Sums over Points of
Elliptic curves with Reciprocals of Primes,
Mathematika, 2012, v. 58, 2133.
 A. Ostafe and I. E. Shparlinski,
Multiplicative Character Sums and Products of
Sparse Integers in Residue Classes,
Period. Math. Hungarica, 2012, v. 64, 247255.
 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, 131143.
 A. Ostafe, D. Thomson and A. Winterhof, On the Waring problem with
multivariate Dickson polynomials,
Finite fields and applications, Contemp. Math., 2012, v. 579, 153161.
 A. Ostafe and I. E. Shparlinski,
On the Waring problem with Dickson polynomials in finite fields,
Proc. Amer. Math. Soc., 2011, v.139, 38153820.
 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, 127142.
 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, 15571571.
 A. Ostafe and I. E. Shparlinski,
Twisted exponential sums over points of elliptic curves,
Acta Arith., 2011, v. 148, 7792.
 A. Ostafe and I. E.
Shparlinski,
Pseudorandomness and dynamics of Fermat quotients,
SIAM J. Discr. Math., 2011, v. 25, 5071.
 A. Ostafe, E. Pelican and I. E. Shparlinski,
On pseudorandom numbers from multivariate polynomial systems,
Finite Fields and Their Appl., 2010, v.16, 320328.
 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, 369379.
 A. Ostafe
and I. E. Shparlinski,
On the length of critical orbits
of stable
quadratic
polynomials,
Proc. Amer. Math. Soc., 2010, v. 138, 26532656.
 A. Ostafe and I. E. Shparlinski,
Pseudorandom numbers and hash
functions
from iterations of multivariate polynomials,
Cryptography and Communications, 2010, v. 2, 4967.
 A. Ostafe,
Multivariate permutation
polynomial systems and
nonlinear pseudorandom number
generators,
Finite Fields and Their Appl.,
2010, 144154.
 Z. Chen, A. Ostafe and A. Winterhof,
Structure of pseudorandom numbers derived from Fermat quotients,
Lect. Notes in Comp. Sci., SpringerVerlag,
Berlin, 2010, 7385.
 A. Ostafe,
Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers,
Lect. Notes in Comp. Sci., SpringerVerlag,
Berlin, 2010, 6272.
 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, 501511.
 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, 501513.
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.
 2021: Session for 2nd year students: Ray Li (University of Cambridge), Link to slides , Link to recording
 2020: Session for 2nd year students: Ray Li (UNSW), Link to slides
Session for 3rd & 4th year students:
Applying in Australia: Ian Doust (UNSW), Link to slides
Applying in USA: Ray Li (UNSW), Link to slides
Applying in UK: Marley Young (University of Cambridge), Link to slides
 2019:
Applying in Australia: Ian Doust (UNSW), Link to slides
Applying in USA & UK: Marley Young (UNSW), Link to notes
 2018:
Applying in USA & UK: Peter Bradshaw (UNSW), Link to notes
Applying in Australia: David Warton (UNSW), Link to slides
Teaching
 2024: MATH3431 (Number Theory)
 2023: MATH2099 (Linear Algebra), MATH5645 (Algebraic Number Theory)
 2022: MATH1141 (Algebra), MATH2099 (Linear Algebra)
 2021: MATH2099 (Linear Algebra), MATH5645 (Algebraic Number Theory)
 2020: MATH1141 (Algebra), MATH5725 (Galois Theory)
 2019: MATH1141 (Algebra), MATH5645 (Algebraic Number Theory)
 2018: MATH1141 (Algebra), MATH1131 (Calculus), MATH5725 (Galois Theory)
 2017: MATH1141 (Algebra), MATH5645 (Algebraic Number Theory)
 2015: MATH5645 (Finite Fields and Applications)  jointly with I. Shparlinski and A. Zumalacarregui