In this work, dedicated to the modular group PSL (2; Z), we investigate several arithmetical
and topological structures underlying its set of conjugacy classes, such as equivalence …

We prove that both stated skein algebras and their reduced versions at odd roots of unity are
almost-Azumaya and compute the rank of a reduced stated skein algebra over its center …

The modular group PSL (2; Z) acts on the hyperbolic plane HP with quotient the modular
surface M, whose unit tangent bundle U is a 3-manifold homeomorphic to the complement of …

We study the space of measured laminations ML on a closed surface from the valuative
point of view. We introduce and study a notion of Newton polytope for an algebraic function …

We study the space of measured laminations ML⁡ on a closed surface from the valuative
point of view. We introduce and study a notion of Newton polytope for an algebraic function …

We study a compact family of totally elliptic representations of the fundamental group of a
punctured sphere into PSL (2, R), discovered by Deroin and Tholozan and named after …

These notes 1 are an extended version of a series of mini-courses that I gave in the spring of
2022 at the KIT Karlsruhe and at the University of Heidelberg and in the spring of 2024 at …