Variation of the Hausdorff dimension of limits set and degenerating Schottky groups

Orateur:
Nguyen-Bac Dang
Localisation: Université Paris-Saclay
Type: Séminaire COOL
Site: IHP
Salle:
Olga Ladyjenskaïa (ex-salle 01)
Date de début:
11/04/2025 - 11:20
Date de fin:
11/04/2025 - 12:20

In this talk, based on a joint work with Vlerë Mehmeti, I will  explain how one can use some techniques in non-Archimedean geometry to study families of  degenerating complex Schottky groups. More precisely, each Schottky group comes with a fractal set, obtained as a limit of an orbit, called the limit set. We show that under specific conditions,  one can can obtain an asymptotic formula for  the Hausdorff dimension of the limit set. If time permits, I will present how certain functions, called Poincare series have very special  behavior when one works over non-Archimedean fields.