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Statut |
Confirmé |
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Série |
MATH-IHES |
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Domaines |
math |
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Date |
Jeudi 2 Mai 2024 |
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Heure |
14:30 |
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Institut |
IHES |
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Salle |
Amphithéâtre Léon Motchane |
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Nom de l'orateur |
Drappeau |
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Prenom de l'orateur |
Sary |
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Addresse email de l'orateur |
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Institution de l'orateur |
Université d’Aix-Marseille |
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Titre |
Quantum Modularity for the q-Pochhammer Symbol |
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Résumé |
The talk will focus on quantum modularity relations satisfied by the q-Pochhammer symbol $(q)_N = (1-q) ... (1-q^N)$ at $q=\exp(2 \pi i x)$. These formulas can be interpreted as finite analogues of the usual modularity for the Dedekind eta-function. We'll discuss certain aspects which come very handy upon summing over $N$. We'll explain how these can be used, in the context of Kashaev's invariant of hyperbolic knots, to prove, in a few cases, Zagier's quantum modularity conjecture by means of what we currently know on the Volume Conjecture. This is based on joint work with Sandro Bettin. |
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Numéro de preprint arXiv |
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Commentaires |
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Fichiers attachés |
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