Pure Maths Colloquium: Discrete groups in complex hyperbolic geometry
30 April 2012 16:00 in CM221
The complex hyperbolic space can be seen as the unit ball in C^n equipped with a metric that generalises the Poincaré metric on the unit disc in C. Discrete groups in PU(n,1) are therefore a generalisation of Fuchsian groups, well known in the frame of uniformisation of Riemann surfaces. However, as soon as the dimension is bigger or equal 2, it becomes much harder to describe discrete groups.
In this talk, I will give a description of the complex hyperbolic plane (n=2), describe examples of the construction of such discrete groups in PU(2,1), and try to present some of the main questions in the field.
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