PhD Defense: Inequalities for the overpartition function

In this talk, we shall study inequalities for the overpartition function, a generalization of the partition function. The central theme of this talk is how the study of such family of inequalities arises from real rootedness properties of certain polynomials, so called Jensen polynomials which amounts to say the log-concavity property, more generally higher order log-concavity property for the overpartition function. We shall also discuss the consequences of studying these properties; for example, the higher order Turan inequalities for the overpartition function. In another direction, we will see the behaviour of finite differences of logarithm of the overpartition function by solving a problem due to Wang and Xie and consequently, will study the log-convexity property of sequences associated with the overpartition function. In the end, we will discuss what has been accomplished and what remains to study as a future prospective.

Zoom-Link:

https://jku.zoom.us/j/94271692912?pwd=R1dSZEVERVI4V056SWk5UkJFYXZNUT09

Meeting-ID: 942 7169 2912

Passwort: 450130