Equations, rational sets and formal languages

Abstract: The set of solutions to a system of equations over a group is known as an algebraic set. The study of such sets goes back to the 1970s and 1980s and work of Makanin and Razborov. More recently, there has been a significant amount of effort to describe algebraic sets in various classes of groups using formal languages, and in particular the class of EDT0L languages. I will explain what an EDT0L language is and describe some recent results on virtually abelian groups. Namely that their algebraic sets can be represented by EDT0L languages (joint work with A. Levine), and that the same is true for their rational sets, those sets described by finite state automata (joint work with L. Ciobanu).

algebraic topologyfunctional analysisgroup theorygeometric topologyoperator algebras

Audience: researchers in the topic

Vienna Geometry and Analysis on Groups Seminar