turkmath.org

In this talk I will discuss new constructions of semigroup actions and monoid actions on sets via biactions, and introduce a method to invert such an action by using them. This point of view allow us to use homotopy theory in the category of semigroup actions, and allow us to construct Burnside ring of a monoid. I will show that for groups this Burnside ring coincides to the usual one, and will show that for a commutative monoid it is equivalent to Burnside ring of its Gröthendieck group. Finally, I will discuss some applications in Automata theory. This is a joint work with Özgün Ünlü.