Computational methods in nonassociative algebra

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The unifying theme of this research program is the developing connections between abstract algebra, computer science, and mathematical genetics. In abstract algebra, the focus is on using computational methods to study the classical theory of polynomial identities for nonassociative algebras.  Most of the classes of algebras studied by mathematicians are defined by identities (such as associative, Lie and Jordan algebras), and many of these structures have applications throughout mathematics and theoretical physics.  I am especially interested in the more recent applications to life sciences (in particular, DNA computing and population genetics) and in applications of biological theory to computer science (in particular, genetic algorithms). My research makes intensive use of computer algebra systems (such as Maple) to implement algorithms from linear algebra, combinatorics, and representation theory (of the symmetric group and of simple Lie algebras).