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ODE/IM correspondence.

Le : 18/10/2016 14h00
Par : Andrea Raimondo, Università di Bergamo
Lieu : I 103
Lien web :
Résumé : The ODE/IM correspondence is a conjectural and surprising relation between integrable quantum field theories (Integrable Models, IM) and monodromy data of certain linear analytic ODEs, associated to affine Kac-Moody Lie algebras. In the simplest case of the algebra $sl_2$, the related ODE is a Schroedinger equation and the corresponding integrable model is the quantum KdV equation. In the present talk, I will briefly introduce the physical origin and the main contributions to the ODE/IM correspondence, describing in particular the recent proof of the correspondence for the ground state of the integrable model. The techniques used for the proof include the representation theory of simple Lie algebras and affine Kac-Moody algebras, as well as the asymptotic theory of linear ODEs in the complex plane. The talk is based on the following joint works with D.Masoero and D.Valeri: Bethe Ansatz and the Spectral Theory of affine Lie algebra-valued connections I. The simply-laced case. Bethe Ansatz and the Spectral Theory of affine Lie algebra-valued connections II: The non simply-laced case.