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).
- Creutz B. and Voloch JF. (2017) Local-global principles for Weil-Chatelet divisibility in positive characteristic. Mathematical Proceedings 163(2): 357-367. http://dx.doi.org/10.1017/S0305004117000032.
- Amerik E., Kurlberg P., Nguyen KD., Towsley A., Viray B. and Voloch JF. (2016) Evidence for the dynamical Brauer-Manin criterion. Experimental Mathematics 25(1): 54-65. http://dx.doi.org/10.1080/10586458.2015.1056889.
- Patrikis S., Voloch JF. and Zarhin YG. (2016) Anabelian geometry and descent obstructions on moduli spaces. Algebra and Number Theory 10(6): 1191-1219. http://dx.doi.org/10.2140/ant.2016.10.1191.
- Voloch JF. (2016) Generators of finite fields with powers of trace zero and cyclotomic function fields. Portugaliae Mathematica 73(1): 65-70. http://dx.doi.org/10.4171/PM/1976.
- Voloch JF. (2016) Planar surfaces in positive characteristic. São Paulo Journal of Mathematical Sciences (early access online) http://dx.doi.org/10.1007/s40863-015-0011-7.