Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Domaines math-ph
Date Jeudi 18 Avril 2019
Heure 14:00
Institut LPTM
Salle 4.13 St Martin II
Nom de l'orateur Roubtsov
Prenom de l'orateur Volodya
Addresse email de l'orateur
Institution de l'orateur LAREMA Université d'Angers
Titre Non-commutative Calogero–Painlevé systems and Ruijsenaars duality revisited
Résumé All Painlevé equations can be written as a time-dependent Hamiltonian system, and as such they admit a natural generalization to the case of several particles with an interaction of Calogero type (rational, trigonometric or elliptic). Recently, these systems of interacting particles have been proved to be relevant in the study of β-models. An almost two decade old open question by Takasaki asks whether these multi-particle systems can be understood as isomonodromic equations, thus extending the Painlevé correspondence. We give an answer in the affirmative by displaying explicitly suitable isomonodromic Lax pair formulations. The famous Ruijsenaars duality applies to the Calogero–Painlevé I, II, IV and the self-duality phenomena in these systems is discussed.
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