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Short survey based on talk given at the Institut Henri Poincare January 17th 2012, during program on surface groups.
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Gravitational multi-instantons
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On the reduction of connection problems for differential equations with an irregular singularity to ones with only regular singularities, I
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Monodromy preserving deformations of linear differential equations with rational coefficients II
M. Jimbo and T. Miwa · 1981
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The Yang-Mills equations over Riemann surfaces
M.F. Atiyah and R. Bott · 1983
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Loop groups and equations of KdV type
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Studies on the Painlevé equations. III. Second and fourth Painlevé equations, P II P_{{\rm II}} and P IV P_{{\rm IV}}
K. Okamoto · 1986
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Baker functions for compact Riemann surfaces
R. J. Schilling · 1986
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Twisted harmonic maps and the self-duality equations
S. K. Donaldson · 1987
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The self-duality equations on a Riemann surface
N. J. Hitchin · 1987
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Stable bundles and integrable systems
N. J. Hitchin · 1987
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Studies on the Painlevé equations. I. Sixth Painlevé equation P VI P_{{\rm VI}}
K. Okamoto · 1987
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Studies on the Painlevé equations. II. Fifth Painlevé equation P V P_{\rm V}
K. Okamoto · 1987
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Topological quantum field theories
M.F. Atiyah · 1988
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Flat G {G} -bundles with canonical metrics
K. Corlette · 1988
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The construction of ALE spaces as hyper-Kähler quotients
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Isospectral Hamiltonian flows in finite and infinite dimensions, II. Integration of the flows
M.R. Adams, J. Harnad, and J. Hurtubise · 1990
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Hyper-Kähler manifolds
M. F. Atiyah · 1990
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Jacobiennes des courbes spectrales et systémes Hamiltoniens completement intégrables
A. Beauville · 1990
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Harmonic bundles on noncompact curves
C. T. Simpson · 1990
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Hyper-Kähler structure on the moduli space of flat bundles
A. Fujiki · 1991
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Hyper-Kähler manifolds
N. J. Hitchin · 1991
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Moduli of semistable pairs on a curve
N. Nitsure · 1991
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The Painlevé equations and the Dynkin diagrams
K. Okamoto · 1992
Symplectic manifolds and isomonodromic deformations
P. P. Boalch · 2001
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Rational surfaces associated with affine root systems and geometry of the Painlevé equations
H. Sakai · 2001
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Hyper-Kähler metrics from periodic monopoles
S. A. Cherkis and A. Kapustin · 2002
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Periodic monopoles with singularities and 𝒩 = 2 \mathcal{N}=2 super-QCD
S. A. Cherkis and A. Kapustin · 2003
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Wild non-abelian Hodge theory on curves
O. Biquard and P. P. Boalch · 2004
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From Klein to Painlevé via Fourier, Laplace and Jimbo
P. P. Boalch · 2005
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Higgs bundles and local systems
C. T. Simpson · 1992
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Construction of the moduli space of stable parabolic Higgs bundles on a Riemann surface
H. Konno · 1993
Cited alongside, same era.
Dual isomonodromic deformations and moment maps to loop algebras
J. Harnad · 1994
Cited alongside, same era.
Spectral curves and integrable systems
E. Markman · 1994
Cited alongside, same era.
Symplectic geometry on moduli spaces of stable pairs
F. Bottacin · 1995
Cited alongside, same era.
Studies on the Painlevé equations, V, third Painlevé equations of special types
Y. Ohyama, H. Kawamuko, H. Sakai, and K. Okamoto · 2006
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Some geometry of irregular connections on curves, November 2007
P. P. Boalch · 2007
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Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces
P. Etingof, A. Oblomkov, and E. Rains · 2007
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Quivers and difference Painlevé equations
P. P. Boalch · 2009
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The moduli space of cubic threefolds as a ball quotient
D. Allcock, J. A. Carlson, and D. Toledo · 2011
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Riemann–Hilbert for tame complex parahoric connections
P. P. Boalch · 2011
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Simply-laced isomonodromy systems, July 2011
P. P. Boalch · 2011
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Geometry and braiding of Stokes data; Fission and wild character varieties, November 2011
P. P. Boalch · 2011
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Middle convolution and Harnad duality
D. Yamakawa · 2011
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Gravitational instantons from rational elliptic surfaces
H.-J. Hein · 2012
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