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math.QA2026
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…
math.QA2026
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…
math.QA2026
q-Rationals, link invariants and webs
Perrine Jouteur, Hoel Queffelec
We investigate the role of q-rationals in the context of link invariants. This leads us to introduce and study web categories that q-deform Deligne's categories.