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Physics letters. B, ISSN 0370-2693, 2010, Volume 691, Issue 2, pp. 111 - 115
We propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional... 
[formula omitted][formula omitted] gauge theories | [formula omitted] Toda theory | Hitchin systems | D=2 Toda theory | N=2 D=4 gauge theories Hitchin systems | PHYSICS, NUCLEAR | N=2 D=4 gauge theories | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS
Journal Article
Advances in mathematics (New York. 1965), ISSN 0001-8708, 2013, Volume 234, pp. 239 - 403
Journal Article
Advances in mathematics (New York. 1965), ISSN 0001-8708, 2018, Volume 327, pp. 225 - 348
.... It gives rise to a moduli space XPGLm,S, closely related to the moduli space of PGLm-local systems on S, which carries a canonical cluster Poisson variety structure [13... 
Cluster varieties | Motivic Donaldson–Thomas invariants | Canonical bases | REPRESENTATIONS | QUIVERS | Motivic Donaldson-Thomas invariants | POTENTIALS | QUANTUM DILOGARITHM | CATEGORIES | HITCHIN SYSTEMS | MATHEMATICS | DOUBLE BRUHAT CELLS | SPECTRAL NETWORKS | CLUSTER ALGEBRAS
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2016, Volume 165, Issue 15, pp. 2991 - 3042
.... Next, we show that every algebraically integrable system gives rise to a degenerate abelian scheme and discuss applications to Hitchin systems. 
MATHEMATICS | DUALITY | COMPACTIFIED JACOBIANS | Mathematics - Algebraic Geometry
Journal Article
Annals of mathematics, ISSN 0003-486X, 2012, Volume 175, Issue 3, pp. 1329 - 1407
Journal Article
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, ISSN 1815-0659, 2019, Volume 15
the present notes we explain the relationship between Calabi-Yau integrable systems and Hitchin systems based on work by Diaconescu-Donagi-Pantev and the author... 
variations of Hodge structures | Hitchin systems | complex integrable systems | LANGLANDS DUALITY | Calabi-Yau threefolds | PHYSICS, MATHEMATICAL | MODULI
Journal Article
Functional Analysis and Its Applications, ISSN 0016-2663, 10/2018, Volume 52, Issue 4, pp. 316 - 320
... 4 –98, 2018 Original Russian Text Copyright c by O. K. Sheinman Integrable Systems of Algebraic Origin and Separation of V ariables ∗ O. K. Sheinman Received... 
integrable system | Functional Analysis | Analysis | the method of separation of variables | quantum analogue | plane algebraic curve | Poisson bracket | Mathematics | Lagrange interpolation polynomial | hyperelliptic Hitchin systems | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 04/2019, Volume 99, Issue 2, pp. 340 - 341
Journal Article
Theoretical and Mathematical Physics, ISSN 0040-5779, 8/2016, Volume 188, Issue 2, pp. 1121 - 1154
Journal Article
Theoretical and Mathematical Physics, ISSN 0040-5779, 10/2013, Volume 177, Issue 1, pp. 1281 - 1338
We describe a construction of elliptic integrable systems based on bundles with nontrivial characteristic classes, especially attending to the bundle-modification procedure, which relates models... 
integrable system | Theoretical, Mathematical and Computational Physics | Painlevé equation | Hitchin system | Applications of Mathematics | modification of bundles | Physics | INVERSE SCATTERING METHOD | 2ND-ORDER | PHYSICS, MULTIDISCIPLINARY | MOMENT MAPS | MODEL | PHYSICS, MATHEMATICAL | DEFORMATION | CURVES | Painleve equation | PAINLEVE-EQUATION | TOPS | HOLOMORPHIC BUNDLES | ORDINARY DIFFERENTIAL-EQUATIONS
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 02/2014, Volume 25, Issue 2, pp. 1450016 - 1-1450016-20
Donagi and Markman (1993) have shown that the infinitesimal period map for an algebraic completely integrable Hamiltonian system (ACIHS... 
Hitchin system | Higgs bundles | Donagi-Markman cubic | algebraic completely integrable systems | SPECTRAL-CURVES | RIEMANN SURFACE | BUNDLES | VARIETIES | MODULI | ALGEBRAIC MANIFOLDS | MATHEMATICS | INTEGRABLE SYSTEMS | JACOBIANS | DUALITY | GEOMETRY | Bundling | Mathematical analysis | Algebra
Journal Article
International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 04/2017, Volume 14, Issue 4
This paper is about geometric quantization of the Hitchin system. We quantize a Kahler form on the Hitchin moduli space... 
geometric quantization | Hitchin system | Quillen bundle | RIEMANN SURFACE | BUNDLES | PHYSICS, MATHEMATICAL
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2007, Volume 2007
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 05/2014, Volume 79, pp. 1 - 13
We will generalize the Treibich–Verdier theory about elliptic solitons to a Hitchin system by constructing a particular ruled surface and we will propose a generalization of a tangency condition associated with elliptic solitons... 
Elementary transformation | Hitchin system | Elliptic soliton | Tangential cover | Residue section | Ruled surface | MATHEMATICS, APPLIED | SOLITONS | EQUATIONS | PHYSICS, MATHEMATICAL
Journal Article
Russian mathematical surveys, ISSN 1468-4829, 2014, Volume 69, Issue 1, pp. 35 - 118
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 10/2018, Volume 59, Issue 10, p. 102301
...) system is obtained in this article. Starting from the known solutions of the original equations, some solutions to these deformed equations are obtained... 
FIELDS | HITCHIN EQUATIONS | EINSTEIN EQUATIONS | INTEGRABLE SYSTEMS | SU(INFINITY) NAHM EQUATIONS | HEAVENLY SPACES | DUALITY | PHYSICS, MATHEMATICAL | GRAVITY | KNOTS | GEOMETRY
Journal Article
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, ISSN 0016-2663, 10/2019, Volume 53, Issue 4, pp. 291 - 303
This paper describes a class of spectral curves and gives explicit formulas for the Darboux coordinates of the Hitchin systems of types A(l... 
MATHEMATICS | MATHEMATICS, APPLIED | BUNDLES | spectral curve | Darboux coordinates | Hitchin system | VARIABLES | SEPARATION | separation of variables
Journal Article
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2012, Volume 8, p. 095
We describe new families of the Knizhnik-Zamolodchikov-Bernard (KZB) equations related to the WZW-theory corresponding to the adjoint G-bundles of different... 
Integrable system | Hitchin system | KZB equation | Characteristic class | ELLIPTIC-CURVES | integrable system | characteristic class | GEOMETRIC-QUANTIZATION | ZUMINO-WITTEN MODELS | CALOGERO-MOSER SYSTEMS | PHYSICS, MATHEMATICAL | R-MATRICES | PAINLEVE-VI | INTEGRABLE SYSTEMS | ZAMOLODCHIKOV-BERNARD EQUATIONS | MANY-BODY SYSTEMS | HOLOMORPHIC BUNDLES
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 02/2019, Volume 136, pp. 14 - 30
...–Yau orbifolds, over the same base. Their intermediate Jacobian fibration, constructed in terms of equivariant cohomology, is isomorphic to the Hitchin system... 
Calabi–Yau threefolds | Hodge theory | Global quotient stacks | Integrable systems | Hitchin systems | MATHEMATICS | DUALITY | Calabi-Yau threefolds | PHYSICS, MATHEMATICAL
Journal Article
Physics of Particles and Nuclei, ISSN 1063-7796, 1/2009, Volume 40, Issue 1, pp. 93 - 114
In this review we consider the Hitchin integrable systems and their relations with the self-duality equations and twisted super-symmetric Yang-Mills theory in four dimensions... 
Elementary Particles and Nuclei | Physics | HITCHIN SYSTEM | BODY PROBLEMS | PAINLEVE-VI | ALGEBRAS | BUNDLES | SYMMETRY | METRICS | EQUATIONS | DUALITY | MODEL | PHYSICS, PARTICLES & FIELDS
Journal Article
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