8 papers
Nuancing the unicity of -rationals
Perrine Jouteur, Olga Paris-Romaskevich, Alexander Thomas
We prove unicity of -rational numbers up to conjugacy, using character varieties. Despite the unicity, we exhibit a two-parameter family of deformations of rationals with a modu…
Plane geometry of -rationals and Springborn Operations
Perrine Jouteur, Olga Paris-Romaskevich, Alexander Thomas
We study the geometry of -rational numbers, introduced by Morier-Genoud and Ovsienko, for positive real . In particular, we construct and analyse the deformed Farey triangula…
Open problems in billiards and quantitative symplectic geometry
Bernhard Albach, Jean-François Barraud, Misha Bialy +13
This document collects contributions to the Open Problem List in Billiards and Quantitative Symplectic Geometry, compiled following discussions during the workshop ``Billiards and…
Tiling billiards and Dynnikov's helicoid
Olga Paris-Romaskevich
Here are two problems. First, understand the dynamics of a tiling billiard in a cyclic quadrilateral periodic tiling. Second, describe the topology of connected components of plane…
Free actions of large groups on complex threefolds
Serge Cantat, Olga Paris-Romaskevich, Junyi Xie
We classify compact Kähler threefolds with a free group of automorphisms acting freely on .
Automorphisms of compact Kähler manifolds with slow dynamics
Serge Cantat, Olga Paris-Romaskevich
We study the automorphisms of compact Kähler manifolds having slow dynamics. By adapting Gromov's classical argument, we give an upper bound on the polynomial entropy and study its…