### Counting and equidistribution of common perpendiculars: arithmetic applications

**Paulin, F ***(Université Paris-Sud)*

Monday 30 June 2014, 15:00-15:50

Seminar Room 1, Newton Institute

#### Abstract

I will survey several arithmetic applications, obtained in joint works with Parkkonen, of our counting (and simultaneous equidistribution of initial and terminal tangent vectors)
of the common perpendiculars between two closed locally convex subsets of a negatively curved manifold: generalisation of Mertens' formula for imaginary quadratic number fields, counting quadratic irrationals with bounded crossratios, equidistribution of rational points in the Heisenberg group, counting of arithmetic chains in the Heisenberg group with
Cygan diameter bounded from below.

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