
School of Mathematics and Statistics
Paula Cohen
CRNS, University of Science and Technology, Lille.
On some nonarithmetic groups arising from
the monodromy of hypergeometric functions.
Friday 23rd October, 121pm, 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 1dimensional case, all but finitely many of these
monodromy groups are nonarithmetic. In the 2dimensional
case, the list of groups acting discontinuously on the 2ball is finite.
These groups have been studied by PicardTeradaDeligneMostow
and the nonarithmetic examples identified. The beautiful
properties of arithmetic groups are wellknown. But these examples
of hypergeometric nonarithmetic groups are also interesting and we discuss
some of their features and applications in number theory.
