In mathematics, the Hitchin integrable system is an integrable system depending on the choice of a complex reductive group and a compact Riemann surface, introduced by Nigel Hitchin in 1987. It lies on the crossroads of algebraic geometry, the theory of Lie algebras and integrable system theory. It also plays an important role in the geometric Langlands correspondence over the field of complex numbers through conformal field theory.
A genus zero analogue of the Hitchin system, the Garnier system, was discovered by René Garnier somewhat earlier as a certain limit of the Schlesinger equations, and Garnier solved his system by defining spectral curves. (The Garnier system is the classical limit of the Gaudin model. In turn, the Schlesinger equations are the classical limit of the Knizhnik–Zamolodchikov equations).
Almost all integrable systems of classical mechanics can be obtained as particular cases of the Hitchin system or their common generalization defined by Bottacin and Markman in 1994.
In mathematics, the Hitchin integrable system is an integrable system depending on the choice of a complex reductive group and a compact Riemann surface...
Nigel James Hitchin FRS (born 2 August 1946) is a British mathematician working in the fields of differential geometry, gauge theory, algebraic geometry...
1- and 2-dimensions Ice-type model of Lieb Quantum Heisenberg model Hitchinsystem Mathematical physics Soliton Painleve transcendents Statistical mechanics...
Hausel & Thaddeus (2002) explained SYZ conjecture in the context of Hitchinsystem and Langlands duality. The dimensions hp,q of spaces of harmonic (p...
notion of degree for a complex vector bundle over a Riemann surface. HitchinsystemHitchin, Nigel (1987). "The self-duality equations on a Riemann surface"...
Derek K. Hitchins (born 1935) is a British systems engineer and was professor in engineering management, in command & control and in systems science at...
critical points and phase transitions of magnetic systems, in which the spins of the magnetic systems are treated quantum mechanically. It is related to...
specific case of Hitchin integrable systems, when the algebraic curve that the theory is defined on is the Riemann sphere and the system is tamely ramified...
The Cambridge line runs from Cambridge junction north of Hitchin on the East Coast Main Line to Shepreth Branch Junction south of Cambridge on the West...
Lancaster's System. There is one surviving Lancaster-designed British School in Hitchin, Hertfordshire—and this is now run as a museum with an experiential educational...
difference, multidimensional equations and fractional integrable nonlinear systems. The independent variables are a spatial variable x {\displaystyle x} and...
The model was later studied in the two-dimensional case as an integrable system, in particular an integrable field theory. Its integrability was shown by...
Machol System Engineering: An Introduction to the Design of Large-scale Systems, McGraw-Hill, 1957. Hitchins, D. (1997) World Class Systems Engineering...
system that are not performed by any part on its own.: 58 Derek Hitchins defines a system in terms of entropy as a collection of parts and relationships...
Hitchin Rugby Club is a rugby club based in Hitchin, Hertfordshire, England. They currently play in Counties 1 Herts/Middlesex - a league at the 7th level...
are called "Hitchin functional" and Topological string is closely related to Hitchin's ideas on generalized complex structure, Hitchinsystem, and ADHM...
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