# Manchester Geometry Seminar 2010/2011

**Thursday 28 October 2010. ** *The Frank Adams Room (Room 1.212), the Alan Turing Building. 4.15pm*
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Symmetric Singularities and Complex Hyperbolic Reflection Groups

Joel Haddley (University of Liverpool)

`j.a.haddley@liverpool.ac.uk`

A cornerstone of classical singularity theory was the discovery of the connection between holomorphic functions with isolated critical points and groups generated by reflections. In particular, Arnold showed that the monodromy groups of the simple (and simple boundary) singularities are isomorphic to Coxeter groups. A generalisation of these methods (due to Goryunov and others) shows how by considering our functions with respect to some cyclic symmetry, our monodromy groups may in fact be complex. We will describe these methods, and show that their application to an exceptional unimodal singularity yields a complex hyperbolic reflection group.