Address:
School of Mathematics and StatisticsThe University of New South Wales
Sydney NSW 2052
Australia
Office: RC-5112
Email: igor.shparlinski@unsw.edu.au
Telephone: +61 (02) 9385 5281
Education
- M.S. in Mathematics, 1977; Moscow State Pedagogical Institute
- Ph.D. in Mathematics, 1980; Moscow State Pedagogical Institute
Awards
- George Szekeres Medal of the Australian Mathematical Society, 2022.
- Discovery Outstanding Research Award, 2014.
- Fellow of the Australian Academy of Science, 2006.
- Australian Professorial Fellow, 2004.
- Fellow of the Australian Mathematical Society, 2000.
- Medal of the Australian Mathematical Society, 1996.
- Humboldt Professorship, DFG, Germany, 1996.
Areas of Interest
- Number Theory: exponential and character sums, finite fields, smooth numbers, linear recurrence sequences
- Theoretical Computer Science: algorithms, complexity
- Cryptography: number theoretic aspects, elliptic curve cryptography, pseudorandom number generators
- Quantum Computation: number theoretic and combinatorial aspects
Problems on Exponential and Character Sums
Exponential and character sums is one of the most universal number theoretic tools with applications in many several areas of mathematics, coding theory, cryptography and computer science. Here is a list of open problems at various levels of difficulty: some may suite for beginners and will consitute just a short self-contained project, some may requite more significant knowledge and efforts.Editorial Duties
Present
- Finite Fields and their Applications (Elsevier);
- Research in Number Theory (Springer);
- Mathematics of Computation (Amer. Math. Soc.);
- Revista Matematica Complutense (Madrid);
- Contributions to Discrete Mathematics (Univ. of Calgary).
Past
- J. of the Australian Mathematical Society (Aust. Math. Soc.);
- Designs, Codes and Cryptography (Springer);
- J. Mathematical Cryptology (Walter de Gruyter);
- SIAM J. Computing (SIAM).
My Publications
Books:- Computational and algorithmic problems in finite fields, Kluwer AP, 1992.
- (with A. J. van der Poorten and H. G. Zimmer, Editors) Proceedings of The Conference on Number Theoretic and Algebraic Methods in Computer Science, World Scientific, 1995.
- Finite fields: Theory and computation, Kluwer Academic Publishers, 1999.
- Number theoretic methods in cryptography: Complexity lower bounds, Birkhauser, 1999.
- (with S. V. Konyagin) Character sums with exponential functions and their applications, Cambridge Univ. Press, Cambridge, 1999.
- (with K.-Y. Lam, H. Wang and C. Xing, Editors) Proc. Workshop on Cryptography and Computational Number Theory (CCNT'99), Singapore, Birkhauser, 2001.
- (with S. Boztas, Editors) Proc. 14th Symp. on Appl. Algebra, Algebraic Algorithms and Error-Correcting Codes, Melbourne, Springer-Verlag, Berlin, 2001.
- Cryptographic applications of analytic number theory, Birkhauser, 2003.
- (with G. Everest, A. J. van der Poorten and T. Ward ) Recurrence sequences, Amer. Math. Soc., 2003.
- (with G. L. Mullen and D. Panario, Editors) Finite fields and applications, Amer. Math. Soc., 2008.
- (with G. McGuire, G. L. Mullen and D. Panario, Editors) Finite fields: Theory and applications, Amer. Math. Soc., 2010.
- (with J. Borwein and W. Zudilin, Editors) Number theory and related fields, Springer Proceedings in Mathematics & Statistics, vol. 43, Springer-Verlag, Berlin, 2013.
- (with D. Kohel, Editors) Frobenius Distributions: Lang-Trotter and Sato-Tate Conjectures, Amer. Math. Soc., 2016.
- (with S. C. Brenner, C.-W. Shu and D. B. Szyld, Editors) 75 Years of Mathematics of Computation, Amer. Math. Soc., 2020.
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