# Colloquium abstracts

**Dali Shen**

TIFR, Mumbai

October 17, 2019

**Geometric structures on arrangement complements**: In the 80's of last century, Deligne and Mostow studied the monodromy problem of Lauricella hypergeometric functions and gave a rigorous treatment on the subject, which provides ball quotient structures on $mathbb{P}^n$ minus a hyperplane configuration of type $A_{n+1}$. Then some 20 years 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. In this talk, I will briefly review the hypergeometric systems first and then explain how they evolve to the theory of geometric structures on arrangement complements.