 Her 1971 doctoral dissertation, "Mean Cesaro Summability of Laguerre and Hermite Series and Asymptotic Estimates of Laguerre and Hermite Polynomials", concerned Cesàro summation, Laguerre polynomials, and Hermite polynomials; her doctoral advisor was Benjamin Muckenhoupt, the namesake of Muckenhoupt weights.In 1967, before she completed her doctorate, Poiani joined the Saint Peter's University faculty as a mathematics instructor.This was one year after Saint Peter's University had begun admitting women, and Poiani became the university's first female mathematics instructor, and one of only seven women on the university faculty.