Alina Ostafe
Address:
School of Mathematics and Statistics
The University of New South Wales (UNSW)
Sydney NSW 2052
Australia
Office: 4078, Red Centre
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
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
 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.
 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.
 A. Ostafe,
Multivariate permutation
polynomial systems and
nonlinear pseudorandom number
generators,
Finite Fields and Their Appl.,
2010, 144154.
 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
and I. E. Shparlinski,
On the length of critical orbits
of stable
quadratic
polynomials,
Proc. Amer. Math. Soc., 2010, v. 138, 26532656.
 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, E. Pelican and I. E. Shparlinski,
On pseudorandom numbers from multivariate polynomial systems,
Finite Fields and Their Appl., 2010, v.16, 320328.
 A. Ostafe and I. E.
Shparlinski,
Pseudorandomness and dynamics of Fermat quotients,
SIAM J. Discr. Math., 2011, v. 25, 5071.
 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,
Twisted exponential sums over points of elliptic curves,
Acta Arith., 2011, v. 148, 7792.
 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,
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 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,
Exponential Sums over Points of
Elliptic curves with Reciprocals of Primes,
Mathematika, 2012, v. 58, 2133.
 A. Ostafe,
Pseudorandom vector sequences of maximal period generated by polynomial dynamical systems,
Designs, Codes and Cryptography, 2012, v. 63, 5972.
 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.
 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, 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 A. Winterhof, Some applications of character sums,
Handbook of Finite Fields, CRC Press, Eds. G. Mullen and D. Panario, 2013, 170185.
 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. 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, On irreducible divisors of iterated polynomials,
Revista Matematica Iberoamericana, 2014, 11231134.
 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.
 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. GomezPerez, J. Gutierrez and A. Ostafe, Collisions in compositions of triangular polynomial systems and
hash functions', J. Symb. Comp., 2016, v. 72, 182195.
 A. Ostafe and M. Sha, Counting dynamical systems over finite fields, Dynamics and Numbers 2014, Contemp. Math., 2016, v. 669, 187203.
 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, On some extensions of the AilonRudnick theorem, Monatshefte fur Mathematik, 2016, v. 181, 451471.
 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.
 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, Polynomial values in
affine subspaces of finite fields, Journal d'Analyse Mathematique (in press).
 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.
 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, 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, 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).
 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
A. Ostafe and M. Young, On algebraic integers of bounded house and preperiodicity in polynomial semigroup dynamics, Submitted, 2018.
Laszlo Merai, A. Ostafe and I. Shparlinski, Dynamical irreducibility of polynomials in reduction modulo primes, Preprint, 2019.
Grants
 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
Becoming a PhD student: What does it take?
Since 2018 I organise 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.
 2019: A/Prof. Ian Doust ( talk), Mr. Marley Young ( talk)
 2018: Mr. Peter Bradshaw ( talk), Prof. David Warton ( talk)
Teaching Experience
UNSW, Sydney, Australia:
 2019: Lecturer: MATH1141 (Algebra), MATH5645 (Algebraic Number Theory)
Tutor: MATH1151 (Algebra)
 2018: Lecturer: MATH1141 (Algebra), MATH1131 (Calculus), MATH5725 (Galois Theory)
Tutor: MATH1131/1141 (Algebra), MATH1231 (Algebra)
 2017: Lecturer: MATH1141 (Algebra), MATH5645 (Algebraic Number Theory)
Tutor: MATH1131/1141 (Algebra), MATH1231/1241 (Algebra)
 2015: Lecturer: MATH5645 (Finite Fields and Applications)  jointly with I. Shparlinski and A. Zumalacarregui
University of Zurich, Switzerland:

2010: Design and conducting a Student Seminar
on Pseudorandom Sequences

2009: Tutor: Elliptic Curves
 2009: Tutor: Linear Algebra II
 2008: Tutor: Linear
Algebra I