ZMP Seminar Series: Separation of Variables

Winter Term 2024/25

DESY/UHH

See also the Junior ZMP Seminar

Abstract, including references

More literature

Literature

Babelon, Bernard, Talon: Introduction to Classical Integrable Systems

Sklyanin: The Quantum Toda Chain

Sklyanin: Separation of variables: New trends (solv-int/9504001)

Kuznetsov, Nijhoff, Sklyanin: Separation of variables for the Ruijsenaars system (solv-int/9701004)

Derkachov, Korchemsky, Manashov: Separation of variables for the quantum SL(2,R) spin chain (hep-th/0210216)

Seminars

Seminar 1: Classical SoV 1 (Lukas Johannsen)

Lecture notes 1

Seminar 2: Classical SoV 2: Spectral Curve (Jonah Baerman)

Lecture notes 2

Seminar 3: Classical SoV 3: Action-Angle Variables (Albert Bekov)

Lecture notes 3

Seminar 4: Quantum SoV 1: Sklyanin Measure and Baxter TQ equation (Torben Skrzypek)

Lecture notes 4

Seminar 5: Quantum SoV 2: Modern approach and higher rank (Paul Ryan)

Lecture notes 5

Seminar 6: Q-operators from quantum group representations (Christopher Raymond)

Lecture notes 6

Literature:

Seminar 7: Functional Separation of Variables (Paul Ryan)

Lecture notes 7

Seminar 8: Separation of Variable and the Analytic Langlands Correspondence (Federico Ambrosino)

In this talk I will discuss a crucial role played by the Separation of Variable method in the context of the Analytic Langlands program. Indeed, the SoV transform between sl(2) WZW model and Liovuille CFT provides a “quantum” generalization of the Analytic Langlands correspondence. I will explain how this relation makes Langlands computable via CFT methods and allows us to test and verify many conjectures and results proposed in the mathematical literature. I will finish by commenting on how the relation to the Langlands program may provide crucial in constructing systematically the SoV transform for theories based on different Lie Algebras.

Lecture notes 8

Schedule (seminar and colloquium) (see also indico)