
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 sineGordon 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 ]

NovikovVeselov Symmetries of the TwoDimensional $O(N)$ 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 OnePoint Function of the Rational SixVertex 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 LiebThirring 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 DaveyStewartson 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

LeePeng Teo
SIGMA 17 (2021), 083, 40 pages [ abs
pdf ]

SecondOrder 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 SixVertex Model

Vladimir V. Bazhanov, Gleb A. Kotousov, Sergii M. Koval and Sergei L. Lukyanov
SIGMA 17 (2021), 025, 29 pages [ abs
pdf ]

