Title: Generalized hypergeometric functions on the Grassmannian and integrable systems of hydrodynamic type
Speaker: Yuancheng Xie (Ohio State University)
Abstract: In this talk I will describe a connection between generalized hypergeometric functions on the Grassmannian and integrable systems of hydrodynamic type. This talk consists of the following four parts: Symmetries of hydrodynamic-type systems in Riemann invariant form; Generalized hypergeometric functions defined on the Grassmannian and their confluences; Integrable hydrodynamic-type systems and confluences of Lauricella-type hypergeometric functions; Some preliminary results on generalizations to the Grassman Gr(r,n) with r > 2.
A special case of the compatibility conditions of hydrodynamic-type systems in Riemann invariant form leads to Euler-Poisson-Darboux(EPD) system. This system admits Lauricella type hypergeometric functions as solutions, which are special cases of Aomoto-Gel'fand hypergeometric functions defined on the Grassman Gr(r, n) with r=2. In this way each Lauricella type hypergeometric functions gives rise to a hierarchy of integrable systems of hydrodynamic type in Riemann invariant form. The confluences of the classical Gauss hypergeometric functions can be generalized to Aomoto-Gel'fand hypergeometric functions. The confluences of a generalized Lauricella type hypergeometric function also produce hierarchies of integrable systems of hydrodynamic type which are not necessarily in Riemann invariant form anymore. In this talk I will describe these constructions and connections and also some preliminary results on generalizations to the Grassman Gr(r,n) with r>2.
Seminar URL: https://people.math.osu.edu/anderson.2804/gcis/
