*Abstract:* In this talk I will give a general picture of my PhD research. It originates from the Deligne-Mostow theory on the Lauricella F_D functions, which provides ball quotient structures on P^n with respect to a configuration space of type A_{n+1}. Later Couwenberg, Heckman and Looijenga developed it to a more general setting by means of the Dunkl connection, which deals with the geometric structures on projective arrangement complements.My PhD research could be viewed as a parallel project of the Couwenberg-Heckman-Looijengaâ€™s theory, but dealing with the toric case. Inspired by the special hypergeometric system constructed by Heckman and Opdam, we consider a family of connections on a total space, which could be regarded as a toric analogue of the Dunkl connection. I will talk about the flatness of the connections, the hyperbolic structures on the toric arrangement complements induced by those connections. And if time permits, even the ball quotient structures on the toric arrangement complements, a problem we are still working on.