Computational methods in nonassociative algebra

这个研究计划的统一主题是抽象代数、计算机科学和数学遗传学之间的发展联系。在抽象代数中，重点是用计算方法研究非结合代数的多项式恒等式的经典理论。数学家研究的大多数代数类都是由恒等式定义的(如结合代数、李代数和乔丹代数)，其中许多结构在整个数学和理论物理中都有应用。我特别感兴趣的是最近在生命科学中的应用(特别是DNA计算和种群遗传学)以及生物理论在计算机科学中的应用(特别是遗传算法)。我的研究集中使用计算机代数系统(如Maple)来实现来自线性代数、组合学和表示理论(对称群和单李代数的)的算法。

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).