The outside of the Teichmüller space of punctured tori in Maskit's embedding.
On the shape of Bers-Maskit slices.
On the arithmetic of cross-ratios and generalised Mertens’ formulas
We develop the relation between hyperbolic geometry and arithmetic equidistribution problems that arises from the action of arithmetic groups on real hyperbolic spaces, especially in dimension . We prove generalisations of Mertens’ formula for quadratic imaginary number fields and definite quaternion algebras over , counting results of quadratic irrationals with respect to two different natural complexities, and counting results of representations of (algebraic) integers by binary quadratic, Hermitian...
On the closedness of approximation spectra
Generalizing Cusick’s theorem on the closedness of the classical Lagrange spectrum for the approximation of real numbers by rational ones, we prove that various approximation spectra are closed, using penetration properties of the geodesic flow in cusp neighbourhoods in negatively curved manifolds and a result of Maucourant [].
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