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Statut |
Confirmé |
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Série |
SEM-DARBOUX |
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Domaines |
hep-th,math.AG |
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Date |
Jeudi 7 Décembre 2023 |
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Heure |
11:00 |
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Institut |
LPTHE |
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Salle |
bibliothèque du LPTHE, tour 13-14, 4eme étage |
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Nom de l'orateur |
Plamondon |
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Prenom de l'orateur |
Pierre-Guy |
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Addresse email de l'orateur |
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Institution de l'orateur |
Laboratoire de Mathématiques de Versailles |
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Titre |
Configuration spaces from representation theory and cluster theory |
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Résumé |
The space of configurations of n distinct points on a projective line has a rich
structure. For instance, it can be realized as a cluster X-variety, in the
language of Fock--Goncharov. Using the categorification of cluster algebras, this
leads to a nice interpretation in terms of representations of the lineraly
oriented type A quiver: each indecomposable representation defines a variable and
an equation, and the configuration space (or rather, a suitable partial
compactification of it) is the locus of zeroes of these equations.
My aim in this talk will be to explain this construction and to see how it can be
generalized beyond type A. In particular, we will see how various geometric
properties of configuration spaces (such as a face structure) have a
representation-theoretical counterpart (such as tau-tilting reduction). |
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Numéro de preprint arXiv |
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Commentaires |
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Fichiers attachés |
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