Computational Algebra and Number Theory

Research - Groups

• Statistical Analysis and Computation Methods and Stochastic Models
• Symmetry/Integrability Analysis and Computer Algebra for Nonlinear Differential Equations
• Computational Methods for Variational Problems
• Analysis and Simulation of Discrete, Spatially-extended Dynamical Systems
• Computational Algebra and Number Theory
• Computer Algebra Algorithms and Parallel Computing
• Computational Topics in General Relativity, Gauge Theory, Classical Mechanics

Computational Algebra and Number Theory

O. Kihel and Y. Li have expertise in module theory, ring theory, units in group rings, arithmetic of number fields, diophantine equations, elliptic curves and applications to cryptography.

Representative publications

1. Y. Li (with Allen Herman and M.M. Parmenter), “Trivial units for $G$-adapted coefficient rings”, Canadian Mathematical Bulletin (In press,2004).
2. Y. Li, “The normalizer of a metabelian group in its integral group ring”, Journal of Algebra, 256 (2002) 343-351.
3. Y. Li (with M.M.Parmenter), “Hypercentral Units in Integral Group Rings”, Proceedings of The American Mathematical Society,129 (2001),. 2235-2239
4. O. Kihel (with C. Levesque),  On a few diophantine equations related to Fermat’s last theorem,  Canadian Mathematical Bulletin 45 (2002), 247-256.
5. O. Kihel,  Extension dihedrals et courbes elliptiques,  Acta Arithmetica 102 (2002), 309-314.
6. O. Kihel (with C. Levesque),  On the diophantine equation x4 – cy4 = z2 and its associated elliptic curve V2 = U3 - U, Journal Theorie des Nombres Bordeaux (in print).