In the first part of the seminar, I will introduce Calabi's diastasis function, a special Kähler potential defined on real analytic Kähler manifold. Then I will illustrate some of its applications. In the second part, I will apply the properties of the diastasis function to provide a lower and an upper bound for the first eigenvalue of a noncompact real analytic Kähler manifold in terms of diastasis and diastatic entropy.