James B. Wilson Assistant Professor Department of Mathematics Colorado State University 101 Weber Building Fort Collins, CO 80523 Office: 125 Weber Building James.Wilson@ColoState.edu

#### conference on (Groups, Computation, Geometry)

 $x(yz)=(xy)z$ $x^n=0$ $x(y+z)=xy+xz$ $xy=0\Rightarrow x=0 \vee y=0$ group decompositions computation with groups group intersections group varieties p-groups isomorphism enumeration bilinear maps isometry and isotopism adjoints derivations Jordan and Lie algebras computation with algebras nonsingularity semifields I work with groups (the first column). I leave simple groups to better minds, so I guess you could say I'm not a simple minded group theorist. Instead I focus on nilpotence (the second column). For me nilpotence is about bilinearity (the third column) and in the course of study I have re-discovered or introduced various connections between these functions and a wide range of algebras both associative and nonassociative. In an attempt to arrange an ontology (in the sense of Computer Science) for bilinear maps I was lead by categories to products without zero-divisors (the fourth column). Who would have thought that nilpotence would go hand-in-hand with omitting zero-divisors! While I am not an expert in all of these areas I find them fruitful places for questions and results and I hope to learn more -- perhaps from you.