Variation of the Hausdorff dimension of limits set and degenerating Schottky groups (Nguyen-Bac Dang - Université Paris- Saclay))

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

RESUME:  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.