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Équations différentielles motiviques et au–delà

Modular linear differential equations and the classification of Rational CFTs

IHP, salle 314

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In this talk I will revisit the classification of Rational Conformal Field Theories (RCFTs) via the modular differential equations satisfied by its characters.
Using the Unbounded Denominators Conjecture of Atkin and Swinnerton-Dyer I will relate the monodromy of the differential equation to the representation theory of PSL(2,Z/nZ).
This elementary observation permits the construction of a simple program to classify characters of RCFTs up to rank 5.