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In this series of lectures, we (re)view the "geometric method" that reconstructs, from a geometric object: the "spectral curve", an integrable system, and in particular its Tau function, Baker-Akhiezer functions and "current amplitudes", all having an interpretation as CFT conformal blocks.
B. Eynard, R. Belliard, From the quantum geometry of Fuchsian systems to conformal blocks of W algebras , math-ph: arxiv.1907.10543
1907
Earlier work this paper cites.
S. Bergman, M. Schiffer, “Kernel functions and elliptic differential equations in mathematical physics”, Academic Press Inc., Publishers, New York, NY, 1953
1953
Earlier work this paper cites.
Rauch H., Weierstrass points, branch points, and moduli of Riemann surfaces, Comm. Pure Appl. Math
1959
Earlier work this paper cites.
M. Sugawara, T. Hirotaka, A field theory of currents , Physical Review, Vol. 170
1968
Earlier work this paper cites.
Hirota R., Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Phys. Rev. Lett
1971
Earlier work this paper cites.
J.D. Fay, Theta Functions on Riemann Surfaces , Lecture Notes in Mathematics, Springer Berlin Heidelberg, Vol. 352
1973
Earlier work this paper cites.
Its A., Matveev V., Schrödinger operators with finite-gap spectrum and N-soliton solutions of the Korteweg-de Vries equation, Teor. Mat. Fiz
1975
Earlier work this paper cites.
Krichever I., Methods of algebraic geometry in the theory of non linear equations, Russ. Math. Surv
1977
Earlier work this paper cites.
Sato, M., Miwa, T., Jimbo, M. (1978). Holonomic quantum fields I. Publications of the Research Institute for Mathematical Sciences, 14(1), 223-267
1978
Earlier work this paper cites.
Sato, M., Miwa, T., Jimbo, M. (1979). Holonomic Quantum Fields. II—The Riemann-Hilbert Problem—. Publications of the Research Institute for Mathematical Sciences, 15(1), 201-278
1979
Earlier work this paper cites.
Sato, M., Miwa, T., Jimbo, M. (1979). Holonomic quantum fields III. Publications of the Research Institute for Mathematical Sciences, 15(2), 577-629
1979
Earlier work this paper cites.
Sato, M., Miwa, T., Jimbo, M. (1979). Holonomic quantum fields. IV. Publications of the Research Institute for Mathematical Sciences, 15(3), 871-972
1979
Earlier work this paper cites.
Sato, M., Miwa, T., Jimbo, M. (1980). Holonomic quantum fields. V. Publications of the Research Institute for Mathematical Sciences, 16(2), 531-584
1980
Earlier work this paper cites.
Dubrovin B., Theta functions and non-linear equations, Russ. Math. Surv
1981
Earlier work this paper cites.
M. Jimbo, T. Miwa and K. Ueno, Monodromy preserving deformation of linear ordinary differential equations with rational coefficients I. General theory and τ \tau -function , Physica 2D, Vol. 2
1981
Earlier work this paper cites.
Jimbo M., Miwa T., Ueno K., Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II, Physica D
1981
Earlier work this paper cites.
Jimbo M., Miwa T., Ueno K., Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. III, Physica D
1981
Earlier work this paper cites.
Lax P., Levermore C., The small dispersion limit of the Korteweg-de Vries equation. I, II, III, Comm. Pure Appl. Math
1983
Earlier work this paper cites.
Sato M., Sato Y., Soliton equations as dynamical systems on infinite-dimensional Grassmann manifold, in Nonlinear partial differential equations in applied science, Stud. Math
1983
Earlier work this paper cites.
Mumford D., Tata lectures on Theta, Modern Birkhäuser Classics, Birkhäuser, Boston, 1984, volume I (no. 28), II (no. 43), III (no. 97)
1984
Earlier work this paper cites.
N. Hitchin, Stable bundles and integrable systems , Duke Mathematical Journal, Vol. 54
1987
Cited alongside, same era.
Riemann Surfaces
I. Kra H. M. Farkas · 1992
Cited alongside, same era.
Krichever I., Perturbation theory in periodic problems for two-dimensional integrable systems, Soviet Scientific Reviews/Section C, Mathematical Physics Reviews
1992
Cited alongside, same era.
Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes
M. Bershadsky, S. Cecotti, H. Ooguri, and C. Vafa · 1994
Cited alongside, same era.
Krichever I., The tau function of the universal Whitham hierarchy, matrix models and topological field theories, Comm. Pure Appl. Math
1994
Cited alongside, same era.
2012
Later among the works it cites.
2012
Later among the works it cites.
V. Bouchard, B. Eynard, ”Think globally, Compute Locally”, math-ph: arxiv.1211.2302, Journal of High Energy Physics, February 2013, 2013:143
2013
Later among the works it cites.
L. Chekhov, B. Eynard, S. Ribault, Seiberg-Witten equations and non-commutative spectral curve in Liouville theory, J. Math. Phys. 54, 022306 (2013), math-ph: arxiv.1209.3984
2013
Later among the works it cites.
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1995
Cited alongside, same era.
I.K. Kostov, Bilinear Functional Equations in 2D Quantum Gravity, arXiv:hep-th/9602117 Workshop on ”New Trends in Quantum Field Theory”, 28 August - 1 September 1995, Razlog, Bulgaria
1995
Cited alongside, same era.
P. Dorey, R. Tateo, Differential equations and integrable models : the SU(3) case , Nuclear Physics B, Vol. 571
2001
Cited alongside, same era.
Dubrovin B., Krichever I., Novikov S., Integrable systems I, Encyclopaedia Math. Sci
2001
Cited alongside, same era.
Babelon O., Bernard D., Talon M., Introduction to classical integrable systems, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 2002
2002
Cited alongside, same era.
B. Eynard and N. Orantin, “Invariants of algebraic curves and topological expansion,” Comm. Numb. Theor. Phys. 1
2007
Cited alongside, same era.
2008
Cited alongside, same era.
2013
Later among the works it cites.
2014
Later among the works it cites.
O. Dumitrescu, M. Mulase, Quantum Curves for Hitchin Fibrations and the Eynard-Orantin Theory , Letters in Mathematical Physics, Vol. 104
2014
Later among the works it cites.
2014
Later among the works it cites.
B. Eynard, S. Ribault, Lax matrix solution of c=1 conformal field theory, JHEP February 2014, 2014:59, math-ph: arxiv.1307.4865
2014
Later among the works it cites.
G. Borot, B. Eynard, All order asymptotics of hyperbolic knot invariants from non-perturbative topological recursion of A-polynomials , math-ph: arxiv.1205.2261, EMS Quantum Topology, Volume 6, Issue 1, 2015, pp. 39–138 DOI: 10.4171/QT/60
2015
Later among the works it cites.
2015
Later among the works it cites.
2015
Later among the works it cites.
M. Manabe, P. Sułkowski, Quantum curves and conformal field theory , math-ph/1512.05785 , 2015
2015
Later among the works it cites.
M. Mulase, P. Sulkowski, Spectral curves and the Schrödinger equations for the Eynard-Orantin recursion , Advances in Theoretical and Mathematical Physics
2015
Later among the works it cites.
P. Norbury, Quantum curves and topological recursion , Proceedings of Symposia in Pure Mathematics, Vol. 93
2015
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2016
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V. Bouchard, B. Eynard, Reconstructing WKB from topological recursion , math-ph/1606.04498 , 2016
2016
Later among the works it cites.
B. Eynard, ”Counting surfaces”, Birkhäuser, (2016) CRM Aisenstadt lectures
2016
Later among the works it cites.
K. Iwaki, Quantum Curve and the First Painlevé Equation , SIGMA, Vol. 12
2016
Later among the works it cites.