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Counting and equidistribution of common perpendiculars: arithmetic applications

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Interactions between Dynamics of Group Actions and Number Theory

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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