Integrable Systems seminar

[Boris Dubrovin]

The next seminar on Integrable Systems will take place
on Wednesday, February 24 at 14:30 - 16:00, Room 136
of SISSA Main Building

Speaker: Andrea RAIMONDO (Univ. Bergamo)

Title: Bethe Ansatz and the spectral theory of affine Lie algebra-valued connections

Abstract: The ODE/IM correspondence is a relation between a class of affine Lie algebra-valued connections — leading to systems of linear ODEs — and certain algebraic equations, known as Bethe Ansatz and related to quantum Integrable Models. In the simplest case of the algebra sl_2, the related ODE is a Schroedinger equation and the corresponding Bethe Ansatz is (strictly related with) the vacuum eingenvalue of the quantum KdV equation. In this talk, I will describe the results achieved in in collaboration with Davide Masoero and Daniele Valeri in the papers http://arxiv.org/abs/1501.07421 <http://arxiv.org/abs/1501.07421> and http://arxiv.org/abs/1511.00895 <http://arxiv.org/abs/1511.00895> , where the ODE/IM correspondence was proved. 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.

Boris Dubrovin