The research deals with basic computational problems for groups. A central theme involves graph-isomorphism testing and related issues. Polynomial-time results as well as other complexity theoretic issues are being extended to matrix groups, the common domain for applications in the mathematical sciences. Implementation and experimentation is accompanying the theory, and both the permutation-group and new matrix-group methods are being efficiently implemented so that the guaranteed asymptotic timings are retained. The same group-theoretic problems are relevant to a new approach to constraint-satisfaction problems that exploits symmetries and can augment existing applied systems.
