An analytic view of transcendence

Abstract: 

In this talk I will survey some of my recent work with various collaborators on transcendence and algebraic independence. In particular, I will talk about possible invariants and eigenvalues for Mahler functions, as well as the strengthening of some classical results in the transcendental theory of power series due in the style of Carlson, Fatou,  Polya, and Szego.