Reciprocal geodesics and dihedral subgroups of lattices in PSL(2, R)

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• Viveka Erlandsson (Bristol)
• Wednesday 23 November 2022, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Oscar Randal-Williams.

I will discuss the growth of the number of infinite dihedral subgroups of lattices in PSL . Such subgroups exist whenever the lattice has 2-torsion and they are related to so-called reciprocal geodesics on the corresponding quotient orbifold. These are closed geodesics passing through an even order orbifold point, or equivalently, homotopy classes of closed curves having a representative in the fundamental group that’s conjugate to its own inverse. We obtain the asymptotic growth of the number of reciprocal geodesics (or infinite dihedral subgroups) in any orbifold, generalizing earlier work of Sarnak and Bourgain-Kontorivich on the growth of the number of reciprocal geodesics on the modular surface. Time allowing, I will explain how our methods also show that reciprocal geodesics are equidistributed in the unit tangent bundle. This is joint work with Juan Souto.

This talk is part of the Differential Geometry and Topology Seminar series.

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