Schur functions in noncommuting variables

In 2004 Rosas and Sagan asked whether there was a way to define a basis in the algebra of symmetric functions in noncommuting variables, NCSym, having properties analogous to the classical Schur functions, in the algebra of symmetric functions, Sym. Despite attempts, this question has remained open since then. In this talk we answer this question by introducing Schur functions in noncommuting variables, which naturally refine Rosas-Sagan Schur functions, in addition to having many analogous classical properties that we will discuss.