FMI Colloquium, December 15 2023

On December 15th 2023 at 17:00 in FMI, hall 325 meeting of the FMI Colloquium will be held.

Prof. Dmitrii Karp, Holon University, Israel is going to give a research presentation on topic: Hyperbolicity and other properties of hypergeometric combinatorial polynomials

In the talk we will discuss d-dimensional (or generalized) Narayana polynomials, whose coefficients count several important combinatorial objects.  Starting with the  hypergeometric generating function of these polynomials, we present analytical proofs of their many known and even some new properties.  This discussion will be shown to be closely related to some questions about the reality of zeros of entire hypergeometric functions.   Next, we will turn our attention to polynomials arising when studying log-concavity of factorial series.  We will discuss  positivity of their coefficients in monomial basis and conjectures regarding their hyperbolicity.  Finally, we will exhibit some combinatorial identities discovered in this log-concavity studies.

This presentation is based on joint work with Anna Vishnyakova, Sergei Kalmykov, Sergei Sitnik  and Yi Zhang.