The hypergeometric groups are the subgroups of $GL_n(C)$ generated by the companion matrices of two monic coprime polynomials of degree $n$ and when the hypergeometric groups are infinite their Zariski closures (inside $GL_n(C)$) are either the symplectic or the orthogonal groups. In this talk we present the progress on the question to determine the arithmetic or thin hypergeometric groups.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/246