My research is primarily in the area of Number Theory, which is the discipline that studies properties of the integers. In particular, I study Diophantine equations, which are polynomial equations in many variables whose solutions are sought among the integers. Algebraic Geometry is the area of Mathematics that studies the geometric objects defined by polynomial equations and they play a fundamental role in my research. A spinoff of this research consists of applications to Cryptography (the study of encryption, which protects information from malicious attacks) and Coding Theory (which is the study of methods for protecting telecommunication against random errors).
- Ostafe A., Shparlinski IE. and Voloch JF. (2023) Equations and Character Sums with Matrix Powers, Kloosterman Sums over Small Subgroups, and Quantum Ergodicity. International Mathematics Research Notices 2023(16): 14196-14238. http://dx.doi.org/10.1093/imrn/rnac226.
- Ostafe ALINA., Shparlinski IE. and Voloch JF. (2023) Weil Sums over Small Subgroups. Mathematical Proceedings of the Cambridge Philosophical Society http://dx.doi.org/10.1017/S0305004123000415.
- Creutz B. and Voloch JF. (2022) The Brauer-Manin obstruction for constant curves over global function fields. Annales de l'Institut Fourier 72(1): 43-58. http://dx.doi.org/10.5802/aif.3473.
- Sheekey J., Van De Voorde G. and Voloch JF. (2022) ON THE PRODUCT OF ELEMENTS WITH PRESCRIBEDÂ TRACE. Journal of the Australian Mathematical Society 112(2): 264-288. http://dx.doi.org/10.1017/S1446788720000178.
- Booher J. and Voloch JF. (2021) Recovering Affine Curves Over Finite Fields From L-Functions. Pacific Journal of Mathematics 314(1): 1-29. http://dx.doi.org/10.2140/pjm.2021.314.1.