Our monthly meeting will take place on Monday the 28th of February, from 4pm to 6pm (Central European Time). Our speakers will be Davide Masoero and Anton M. Zeitlin. The zoom link will be sent to the members of the project through the mailing list. If you are interested in participating and you are not a PIICQ participant, please register sending us an email!
First talk by Davide Masoero at 4pm
Title: A “proof” of the ODE/IM correspondence for the Quantum KdV model.
Abstract: The Quantum KdV model is a conformal field theory, whose hamiltonian structure is a deformation of the second KdV hamiltonian structure. It is also the conformal (or scaling) limit of the XXZ chain and it is integrable by the Bethe Ansatz Equations. In 1998 Dorey and Tateo discovered that the Bethe roots for the ground state of such a model coincide with the eigenvalues of certain anharmonic oscillators (ODE/IM correspondence). In 2004 Bazhanov-Lukyanov-Zamolodhchikov conjectured that each state of the model corresponds to a “monster potential” (a generalization of an anharmonic oscillator) whose eigenvalues coincide with the Bethe roots. In this talk I provide an outline of the proof – conditional on the existence of a certain Puiseux series – of the BLZ conjecture that I have recently obtained in collaboration with Riccardo Conti.
Second talk by Anton M. Zeitlin at 5pm
Title: Spin chains and geometric structures.
Abstract: I will talk about the geometric aspects of integrable systems, based on Yangians and quantum groups, known as XXX and XXZ spin chain models. Their “classical” limits, the so-called Gaudin models, are related to opers, special classes of connections with regular singularities on the projective line. The key objects in this relation are the Bethe equations: algebraic equations, which on one side describe the spectrum of Gaudin models, and at the other side put constraints on the oper connections. This relation between seemingly unrelated classes of objects emerged around 20 years ago as one of the interesting examples of the geometric Langlands correspondence. In this presentation, I will focus on recent developments, allowing to extend this correspondence to XXX and XXZ models, by introducing the necessary geometric objects, generalizing oper connection. We will start from the geometric setup, leading to the notion of the q-oper. After that, I explain their relation to the spectrum of the XXX and XXZ models, generalizing the Gaudin-oper correspondence. In the end, I will highlight some of the applications of q-opers.