University of Sydney
School of Mathematics and Statistics
CRNS, University of Science and Technology, Lille.
On some non-arithmetic groups arising from
the monodromy of hypergeometric functions.
Friday 23rd October, 12-1pm, Carslaw 273.
For certain parameter choices, the classical
Gauss hypergeometric and Appell hypergeometric functions
give rise to monodromy groups acting discontinuously on
the 1 and 2 dimensional complex balls respectively. In
the 1-dimensional case, all but finitely many of these
monodromy groups are non-arithmetic. In the 2-dimensional
case, the list of groups acting discontinuously on the 2-ball is finite.
These groups have been studied by Picard-Terada-Deligne-Mostow
and the non-arithmetic examples identified. The beautiful
properties of arithmetic groups are well-known. But these examples
of hypergeometric non-arithmetic groups are also interesting and we discuss
some of their features and applications in number theory.