Title: Real complex functions

Abstract: Sarason developed a wonderful structure theory for unbounded Toeplitz operators on the Hardy space. This talk will focus on unbounded symmetric Toeplitz operators which will lead us to a discussion of an interesting class of analytic functions on the unit disk — those which have real boundary values (almost everywhere). These functions have an interesting structure (mapping properties, factorization properties) and it is often the case the the operator theory of the Toeplitz operators can inform the properties of these class of functions (and vice versa).