4 papers
Nuancing the uniqueness of -rationals
Perrine Jouteur, Olga Paris-Romaskevich, Alexander Thomas
We prove uniqueness of -rational numbers up to conjugacy, using character varieties. Despite the uniqueness, we exhibit a two-parameter family of deformations of rationals with…
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…
Spectral Networks: Bridging higher-rank Teichmüller theory and BPS states
Clarence Kineider, Georgios Kydonakis, Eugen Rogozinnikov +2
This book offers a comprehensive introduction to spectral networks from a unified viewpoint that bridges geometry with the physics of supersymmetric gauge theories. It provides the…
Fock bundles and Hitchin components
Georgios Kydonakis, Charlie Reid, Alexander Thomas
We introduce the concept of a Fock bundle, a smooth principal bundle over a surface equipped with a special kind of adjoint-valued 1-form, as a new tool for studying character vari…