Research Interests

My research interests include differential equations and integrability, computer algebra, General Relativity and special aspects of optimization and artificial intelligence.

Work in computer algebra concerns algorithms to simplify and solve overdetermined systems of equations (linear/non-linear), (algebraic/ordinary differential (ODEs)/partial differential (PDEs)). These basic algorithms are applied in higher level programs for the determination of symmetries, conservation laws or other properties of differential equations. Applications include the classification of integrable systems of evolutionary scalar PDEs, vector PDEs, single and systems of supersymmetric evolutionary PDEs and recently integrable quadratic Hamiltonians with higher degree first integrals but also discrete integrable system from Discrete Differential Geometry.

Attempts to increase the efficiency of related programs lead to a study of the parallelization of my algorithms and programs. Currently I am the Brock site leader of the SHARCNET consortium.

An old hobby of mine concerns the computerization of the Asian game of Go. My algorithms and programs specialize on life and death problems in Go.

Computer Algebra Programs