Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Special Issue on Mathematics of Integrable Systems: Classical and Quantum in honor of Leon Takhtajan for his 70th birthday

The Guest Editors for this special issue are

Alexander Its (Indiana University - Purdue University Indianapolis, USA)
Nicolai Reshetikhin (University of California, Berkeley, USA)
Fedor Smirnov (LPTHE, CNRS, University Paris 6, France)

This issue is devoted to integrable systems and their ramifications in modern mathematics. The volume also serves to honor Leon Takhtajan on the occasion of his 70th birthday.

Leon Takhtajan is a world renowned expert in the field – in fact, one of its creators. He has made several groundbreaking contributions to all key developments of integrable systems, both classical and quantum. Among Takhtajan's pioneering results are the establishing of the complete integrability of the classical Nonlinear Shrödinger and sine-Gordon equations and the seminal works, done together with Ludwig Faddeev, Evgeny Sklyanin and Nicolai Reshetikhin, on the algebraic Bethe Ansatz, quantum inverse scattering method, and on quantization of Lie groups and algebras.

In addition to the theory of classical and quantum integrable systems and the theory of quantum groups, Leon Takhtajan has made major contributions in many other areas which include the quantum field theories on algebraic curves, the Poincaré problem of the accessory parameters of Fuchsian uniformization, the local index theorems for a family of Riemann surfaces, a new Kähler metric on module spaces and the spectral theory of automorphic Laplacian and its relation to number theory. This Special Issue is intended to reflect this remarkable broadness of Leon Takhtajan's interests and achievements. The articles of the volume cover a wide range of the topics from the theory of integrable systems per se to the various questions of spectral theory, algebraic geometry, quantum field theory and the theory of quantum groups.

Guest Editors        

Papers in this Issue:

Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study
Claudio Meneses
SIGMA 18 (2022), 062, 41 pages   [ abs   pdf ]
Pullback Coherent States, Squeezed States and Quantization
Rukmini Dey and Kohinoor Ghosh
SIGMA 18 (2022), 028, 14 pages   [ abs   pdf ]
Novikov-Veselov Symmetries of the Two-Dimensional $O(N)$ Sigma Model
Igor Krichever and Nikita Nekrasov
SIGMA 18 (2022), 006, 37 pages   [ abs   pdf ]
Tau Function and Moduli of Meromorphic Quadratic Differentials
Dmitry Korotkin and Peter Zograf
SIGMA 18 (2022), 001, 10 pages   [ abs   pdf ]
Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots
Nikolai Kitanine and Giridhar Kulkarni
SIGMA 17 (2021), 112, 25 pages   [ abs   pdf ]
Boundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties
Mikhail D. Minin and Andrei G. Pronko
SIGMA 17 (2021), 111, 29 pages   [ abs   pdf ]
How to Draw a Correlation Function
Nikolay Bogoliubov and Cyril Malyshev
SIGMA 17 (2021), 106, 35 pages   [ abs   pdf ]
A Sharp Lieb-Thirring Inequality for Functional Difference Operators
Ari Laptev and Lukas Schimmer
SIGMA 17 (2021), 105, 10 pages   [ abs   pdf ]
Liouville Action for Harmonic Diffeomorphisms
Jinsung Park
SIGMA 17 (2021), 097, 16 pages   [ abs   pdf ]
Negative Times of the Davey-Stewartson Integrable Hierarchy
Andrei K. Pogrebkov
SIGMA 17 (2021), 091, 12 pages   [ abs   pdf ]
Resolvent Trace Formula and Determinants of $n$ Laplacians on Orbifold Riemann Surfaces
Lee-Peng Teo
SIGMA 17 (2021), 083, 40 pages   [ abs   pdf ]
Second-Order Differential Operators in the Limit Circle Case
Dmitri R. Yafaev
SIGMA 17 (2021), 077, 13 pages   [ abs   pdf ]
Completeness of SoV Representation for $\mathrm{SL}(2,\mathbb R)$ Spin Chains
Sergey É. Derkachov, Karol K. Kozlowski and Alexander N. Manashov
SIGMA 17 (2021), 063, 26 pages   [ abs   pdf ]
Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model
Vladimir V. Bazhanov, Gleb A. Kotousov, Sergii M. Koval and Sergei L. Lukyanov
SIGMA 17 (2021), 025, 29 pages   [ abs   pdf ]

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