Abstract:
Sets of solutions to systems of equations (varieties) over free associative (non-commutative) algebras
were studied from the 1960's by ring theorists (P.M. Cohn, G. Bergman, and others). Because of the strict failure of
unique factorization over these free algebras, not much is known about these varieties, and no conjectures were
ever made.
We will present our work in progress (partly joint with Agatha Atkarskaya) on the structure of some of these varieties.
The structure that we found is based on our previous work on varieties over free groups and semigroups, and
involves concepts from low dimensional topology with other concepts from commutative algebra.
