Real numbers generated by Finite Automata

Number theorists have long been interested in understanding the complexity of the decimal expansions of classical constants such as $\sqrt{2}$ or $\pi$, as well as in related questions--such as how complexity may emerge from a change of base. Finite automata, viewed as transducers, offer a natural framework to define a class of real numbers that are particularly simple from a computational perspective. This allows us to revisit these classical problems with new tools. 

In this talk, I will survey key results concerning this class of numbers from a number-theoretic viewpoint. In particular, I will describe recent work--joint with Colin Faverjon--that develops a method originally introduced by Mahler in transcendental number theory to address some of these questions.