Fields of interest:

• Diophantine equations (11D) - Diophantine m-tuples, i.e. sets with the property that the product of any two of its distinct elements is one less than a square; Simultaneous Pellian equations; Thue equations and inequalities

• Elliptic curves (11G05) - Construction of high-rank elliptic curves; Integer points on families of elliptic curves

• Diophantine approximations (11J) - Applications of Baker's theory and hypergeometric method; Continued fractions

• Polynomials (11C08) - Indecomposability of polynomials and related Diophantine equations; Polynomial root separation

• Fibonacci and Lucas numbers (11B39) - Diophantine and divisibility properties of binary recursive sequences; Connections with Diophantine m-tuples

• Cryptography (94A60) - Elliptic Curve Cryptography; Cryptanalysis of RSA; Teaching