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.
- Creutz B. and Voloch JF. (2019) Tate-Shafarevich groups of constant elliptic curves and isogeny volcanos. arXiv.
- Creutz B. and Voloch JF. (2019) The Brauer-Manin obstruction for constant curves over global function fields. arXiv.
- Shparlinski IE. and Voloch JF. (2019) Value Sets of Sparse Polynomials. Canadian Mathematical Bulletin : 1-10. http://dx.doi.org/10.4153/s0008439519000316.
- Sutherland AV. and Voloch JF. (2019) Maps between curves and arithmetic obstructions. ARITHMETIC GEOMETRY: COMPUTATION AND APPLICATIONS 722: 167-175. http://dx.doi.org/10.1090/conm/722/14532.