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Shedule -

Équations différentielles motiviques et au–delà

$q$-rationals and dimers

IHP

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The notion of $q$-deformed rational numbers was introduced in our work with Sophie Morier-Genoud. I will explain the relationships between $q$-rationals and the theory of dimer models. I will also discuss a natural $q$-deformation of the classical Markov numbers.

 
The talk will be elementary and accessible to everyone. It is based on two recent preprints, arXiv:2507.19080 (jointly with Sam Evans, Sophie Morier-Genoud, and Perrine Jouteur) and arXiv:2510.16270.