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Vertex models and $E_n$-algebras

Appears in collection : Vertex Algebras and Representation Theory / Algèbres vertex et théorie des représentations

I will explain and state a conjecture of Kontsevich, that relates vertex models from statistical mechanics to $E_n$-algebras (i.e., algebras for the n-dimensional little disks operad). I will also give the main ingredients of the proof of Kontsevich's conjecture, that involve discretized versions of the little disks operad. This is a work in progress with Damien Lejay.

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