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Inaugural Lectures
Research Visitors' Centre, School of Mathematics
University of Leeds
Wednesday 30 September 2009

School of MathematicsProfessor Caroline M. Series
Mathematical Institute, University of Warwick

Insights and vistas in hyperbolic geometry

Abstract: Hyperbolic geometry is like geometry on a leaf of kale. We shall discuss some crucial features of this geometry: for example, the diagonal of a rectangle is little shorter than the sum of the two sides. Hyperbolic geometry has been used to study chaotic dynamics on surfaces, while recent years have seen huge progress in our understanding of hyperbolic structures on three dimensional manifolds.

As will be illustrated in the talk, the infinitely rich world of hyperbolic symmetries leads to graphics as striking for their aesthetic appeal as

for their mathematical content. In particular, the so-called limit sets of hyperbolic symmetry groups are intricate and beautiful fractals.

Abstracting the special features of hyperbolic geometry has led to profound new insights, which in turn have been developed into remarkable new tools for resolving many hitherto unanswered questions about three manifolds and their associated limit sets.

Caroline M. Series' webpage

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Last updated: Wed 30 Jan 2008