Колоквиум на ФМИ, 15 декември 2023

На 15 декември 2023 г. (петък) от 17:00 часа в зала 325 на ФМИ ще се проведе поредната сбирка на Колоквиума на ФМИ. 

Доклад ще изнесе професор Dmitrii Karp, Holon University, Israel.

Тема на доклада:
Hyperbolicity and other properties of hypergeometric combinatorial polynomials

Резюмето на доклада:
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.