Winding of low-lying closed geodesics

Vortrag von Elias Dubno

Datum: 01.04.26  Zeit: 13.30 - 14.30  Raum: ETH HG G 19.1

The winding statistics of closed geodesics on the modular surface depend strongly on how one samples the geodesics: allowing deep excursions into the cusp yields heavy-tailed Cauchy laws, whereas suppressing these excursions produces Gaussian limits. I will explain this transition using continued fraction expansions and the associated digit sums, and discuss results for low-lying geodesics, where geometric length and symbolic length become comparable.