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- Emmy-Noether-Professur 2009
Als achte Emmy-Noether-Professorin wird Prof. Caroline Series (Warwick) vom 19.Oktober bis 6.November 2009 in Göttingen sein. Sie hält drei Vorträge:
Kleinian groups and their limit sets
Abstract: One of the main contributions of Felix Klein, Professor in Göttingen from 1886 until his retirement in 1913, was the theory of Kleinian groups, that is, discrete groups of conformal automorphisms of the Riemann sphere. In recent years this theory has undergone major developments. Kleinian groups are now completely classified by a beautiful geometrical theory which involves the extended action of the group on hyperbolic three space and the geometry and topology of the quotient hyperbolic three manifold.
An important feature of a Kleinian group is its limit set, where the orbits of points accumulate on the Riemann sphere. This concept, introduced by Klein, can now be illustrated by computer graphics, explored by Mumford, Series and Wright in their book Indra's Pearls.
In the first of these three talks, illustrated with many graphics, we follow the book in explaining in an elementary way the meaning of the limit set and how it can be computed. In the other two talks we shall look in detail at Kleinian groups isomorphic to the fundamental group of a surface. These already embody most of the key features of the general theory. We explain how various geometrical features in the three manifolds give rise to limit sets which range from a simple round circles, through circle packings, to space filling curves.
The talks will be an opportunity both to understand the meaning of some of the recent results and also to appreciate many beautiful computer pictures which Klein could only have dreamt about.