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).
- Aubry Y., Herbaut F. and Voloch JF. (2019) Maximal differential uniformity polynomials. ACTA ARITHMETICA 188(4): 345-366. http://dx.doi.org/10.4064/aa170806-11-7.
- SHPARLINSKI IGORE. and VOLOCH JFELIPE. (2019) VALUE SETS OF SPARSE POLYNOMIALS. Canadian Mathematical Bulletin : 1-12. http://dx.doi.org/10.4153/s0008439519000316.
- Bretèche RDL., Sha M., Shparlinski IE. and Voloch JF. (2018) The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves. Mathematische Zeitschrift 290(3-4): 831-855. http://dx.doi.org/10.1007/s00209-018-2042-0.
- Creutz B., Viray B. and Voloch JF. (2018) The d-primary Brauer–Manin obstruction for curves. Research in Number Theory 4(2) http://dx.doi.org/10.1007/s40993-018-0120-3.
- Creutz BM. and Voloch JF. (2017) Local-global principles for Weil-Châtelet divisibility in positive characteristic. Mathematical Proceedings of the Cambridge Philosophical Society 163(2): 357-367. http://dx.doi.org/10.1017/S0305004117000032.