Publications


Spectral theory of Riemann surfaces

A.Kokotov, D.Korotkin, "Tau-functions on spaces of Abelian differentials and higher genus gen-
eralization of Ray-Singer formula
", Journal of Differential Geometry, 82 No.1 35-100 (2009)

C.Klein, A.Kokotov, D.Korotkin, "Extremal properties of determinant of Laplacian in Bergman
metric on the moduli space of genus two Riemann surfaces
", Mathematische Zeitschrift, DOI
10.1007/s00209-008-0314-9 (2008)

A.Kokotov, D.Korotkin, "Normalized Ricci  flow on Riemann surfaces and determinant of Lapla-
cian
", Letters in Mathematical Physics 71 241-242 (2005)

A.Kokotov, D.Korotkin, "Tau-functions on spaces of Abelian and quadratic differentials and
determinants of Laplacians in Strebel metrics of finite volume"
math.SP/0405042, preprint No.
46 of Max-Planck Institut for Mathematics in Science, Leipzig (2004)

Riemann-Hilbert problems, isomonodromic deformations

and Frobenius manifolds

D.Korotkin, V.Shramchenko, "Riemann-Hilbert problems for Hurwitz Frobenis manifolds", Lett.Math.Physics
(2010), volume dedicated to 65th birthday of V.B.Matveev, Vol. 96, No.3 109-121 (2011)

D.Korotkin, V.Shramchenko, "Inverse monodromy problem for Hurwitz Frobenis manifolds:
regular singularities
", J. Reine Agew. Math, Vol. 2011, issue 661, 125-187 (2011)

D.Korotkin, H.Samtleben, "Generalization of Okamoto's equation to arbitrary 2 by 2 Schlesinger
system"
, Advances in Mathematical Physics, Vol. 2009 (2009), Article ID 461860, 14p

A.Kokotov and D.Korotkin, "Isomonodromic tau-function of Hurwitz Frobenius manifolds and
its applications
", International Mathematics Research Notices, 2006 1-34 (2006)

A.Kokotov, D.Korotkin, "Tau-function on Hurwitz spaces", Mathematical Physics, Analysis and
Geometry 7 (2004) no.1 47-96 (2004)

D.Korotkin, "Solution of an arbitrary matrix Riemann-Hilbert problem with quasi-permutation
monodromy matrices"
, Mathematische Annalen 329 No. 2, 335-364 (2004)

A.Kokotov, D.Korotkin, "On G-function of Frobenius manifolds related to Hurwitz spaces", In-
ternational Mathematics Research Notices 2004 no.7 343-360 (2004)

D.Korotkin, "Matrix Riemann-Hilbert problems related to branched coverings of CP1", in \Op-
erator theory: Advances and Applications", 103-129, ed. by I.Gohberg, A.F. dos Santos and
N.Manojlovic, Birkhauser, Boston, (2002)

D.Korotkin, "Isomonodromic deformations and Hurwitz spaces", in 'Isomonodromic Deforma-
tions: theory and applications", ed. by J.Harnad and A.Its, CRM Proceedings and Lecture
Notes, American Mathematical Society (2001)

D.Korotkin, "Isomonodromic deformations in genus zero and one: algebro-geometric solutions
and Schlesinger transformations"
, in "Integrable systems: from classical to quantum", ed. by
J.Harnad, G.Sabidussi and P.Winternitz, CRM Proceedings and Lecture Notes, American Math-
ematical Society (2000)

D.Korotkin, N.Manojlovic and H.Samtleben, "Schlesinger transformations for elliptic isomon-
odromic deformations"
, Journal of Mathematical Physics, 41 3125 (2000)

A.Kitaev, D.Korotkin, "On solutions of Schlesinger equations in terms of theta-functions", In-
ternational Mathematics Research Notices No. 17 p. 877-905 (1998)

D.Korotkin and H.Samtleben, "On the quantization of isomonodromic deformations on the
torus"
, International Journal of Modern Physics A 12 2013-2030 (1997)

Integrable systems and  moduli spaces

D.Korotkin, P.Zograf, "Tau-function and Prym-Tyurin class", submitted to "Contemporary Mathematics" (2012)

D.Korotkin, P.Zograf, "From the tau function of Painlev\'e VI equation
to the geometry of moduli spaces", in "Painle\'e equations and related topics", ed. by A.Bruno and A.Batkhin,
de Gruyter Proceedings in Mathematics,  p. 241-246 (2012)

D.Korotkin and P.Zograf, "Tau-function and moduli of differentials", Mathematical Research Letters,  vol. 18 No.3 (2011)

A.Kokotov, D.Korotkin, P.Zograf, "Isomonodromic tau-function and admissible covers", Advances in Mathematics, 
vol. 227 Issue. 1, p.586-600 (2011)

A.Kokotov, D.Korotkin, "The invariant Wirtinger projective connection and tau-functions on
the Hurwitz spaces", CRM Proceedings and Lecture Notes, 91-97 (2004), ed. by P.Winternitz
and P.Tempesta

Intergrable systems: other

D.Korotkin, V.Shramchenko, ``On higher genus  Weierstrass sigma-function'', 
Physica D http://dx.doi.org/10.1016/j.physd.2012.01.002 (2012)

A.Kokotov, D.Korotkin, "A new hierarchy of integrable systems associated to Hurwitz spaces",
Philosophical Transactions of Royal Society A 10.1098/rsta.2007.2061 (2007)

A.Kokotov, D.Korotkin, V.Shramchenko, "Non-autonomous integrable systems associated to
Hurwitz spaces of genus zero and one"
, Theoretical and Mathematical Physics, 137 no.1 153-160
(2003)

D.Korotkin, "On some integrable cases in surface theory", Zapiski Nauchnih Seminarov LOMI:
"Differential geometry, Lie groups and mechanics" 234 65-125 (1996) english translation: Journal
of Mathematical Sciences 94 1177{1217 (1999)

D.Korotkin, "Self-duality equations: monodromy matrices and algebraic curves", Zapiski Nauch-
nih Seminarov LOMI, 14 197-216 (1994), english translation: Journal of Mathematical Sciences
(New York) 85 1684{1697 (1997)

D.Korotkin, V.Reznik, "Bianchi surfaces in R^3 and deformations of hyperelliptic curves", Matem-
aticheskije Zametki, 52, No.3 78-88 (1992); english translation: Mathematical Notes 52 930-937
(1993)

D.Korotkin, "Finite-gap solutions of the axisymmetric Heisenberg magnetic", Matematicheskije
Zametki, 47, No.2 77-79 (1991)

D.Korotkin, "Self-dual Yang-Mills  fields and deformations of algebraic curves", Communications
in Mathematical Physics 134, 397-412 (1991)

D.Korotkin, "Finite-gap solutions of SU(1,1) and SU(2) Self-Duality equations and their axisym-
metric stationary reductions"
, Matematicheskij Sbornik, 181, 923-933 (1990); english translation:
Mathematics in USSR (Sbornik) 70 355-366 (1991)

D.Korotkin, V.Matveev, "Finite-gap integration of nonlinear differential equations having U-V
pairs with a variable spectral parameter", in \Some topics on inverse problems" (Montpellier,
1987), 182-211, ed. by P.Sabatier, World Scieti¯c Publishing, Singapore (1988)

Matrix models

A.Kokotov and D.Korotkin, "Bergman tau-function: from random matrices and Frobenius man-
ifolds to spaces of quadratic differentials"
, Journal of Physics A, Mathematical and General, 39
8997-9014 (2006)

B.Eynard, A.Kokotov, D.Korotkin, "1/N^2 correction to free energy in hermitian two-matrix
model
", Letters in Mathematical Physics, 71 199-207 (2005)

B.Eynard, A.Kokotov, D.Korotkin, "Genus one contribution to free energy in Hermitian two-
matrix model"
, Nuclear Physics B694 443-472 (2004)

Exact solutions of Einstein's equations

D.Korotkin, Review of the book "Ernst equation and Riemann surfaces: analytical and numerical
methods" by C.Klein and O.Richter, General Relativity and Gravitation v.39 pp. 695-697 (2007)

C.Klein, D.Korotkin, V.Shramchenko, "Ernst equation, Fay identities and variational formulas
on algebraic curves
", Mathematical Research Letters 9 No.1 27-46 (2002)

 E.Ferapontov, D.Korotkin and V.Shramchenko, "Boyer-Finley equation and systems of hydro-
dynamic type"
, Classical and Quantum Gravity, 19 L205-L210 (2002)

D.Korotkin, V.Matveev, "Theta function solutions of the Schlesinger system and the Ernst equa-
tion"
, Funkcionalnij Analiz i ego prilojenija, 34 No.4 18-34 (2000) (english translation: Func-
tional Analysis and Its Applications, 34 252-264 (2000))


D.Korotkin and V.Matveev, "Schlesinger system, Einstein equations and hyperelliptic curves",
Letters in Mathematical Physics, 49 145-159 (1999)

M.Babich and D.Korotkin, "Self-dual SU(2) invariant Einstein metrics and modular dependence
of theta-functions"
, Letters in Mathematical Physics 46 323-337 (1998)

D.Korotkin, "Some remarks on finite-gap solutions of the Ernst equation", Physics Letters A
229 195-199 (1997)

D.Korotkin and H.Nicolai, "Black hole in a periodic Kasner Universe", "Gauge Theories, Ap-
plied Supersymmetry, Quantum Gravity", ed. by B. De Wit et al, Leuven University Press
283-288 (1996)

D.Korotkin and H.Nicolai, "The Ernst equation on a Riemann surface", Nuclear Physics B429, 229-254 (1994)

D.Korotkin, "On the link between different U-V pairs and related  finite-gap solutions of the
stationary axisymmetric Einstein equation", Journal of Physics A 26 3823-3836 (1993)

D.Korotkin, "Elliptic solutions of stationary axisymmetric Einstein equation", Classical and
Quantum Gravity 26 2587-2613 (1993)

D.Korotkin, "Solutions of the vacuum Einstein equation having toroidal infinite redshift surface",
Classical and Quantum Gravity 8 L219-L222 (1991)

D.Korotkin, "Algebro geometric solutions of the Einstein equation: Some physical properties",
Communications in Mathematical Physics 137 383-398 (1991)

D.Korotkin, V.Matveev, "Algebro-geometric solutions of gravitational equations", Algebra i
Analiz 1 no. 2, 77-102 (1989); english translation: Leningrad Mathematical Journal 1 379-
408 (1990)

D.Korotkin, "Finite-gap solutions of stationary axisymmetric Einstein equations in vacuum",
Teoreticheskaya i Matematicheskaya Fizika, 77 No.1 pp.25-41 (1988); english translation: The-
oretical and Mathematical Physics, 77 1018-1031 (1989)

Integrable models of quantum gravity

D.Korotkin and H.Samtleben, "Yangian symmetry in integrable quantum gravity", Nuclear
Physics B, 527 657-689 (1998)

D.Korotkin, H.Samtleben, "Canonical quantization of cylindrical gravitational waves with two
polarizations"
, Physical Review Letters 80 14-17 (1998)

D.Korotkin and H.Samtleben, "Quantization of coset-space sigma-model coupled to 2D gravity",
Communications in Mathematical Physics, 190 411-457 (1997)

D.Korotkin and H.Samtleben, "Poisson Realization and Quantization of the Geroch group",
Classical and Quantum Gravity, 14, L151-L156 (1997)

D.Korotkin and H.Nicolai, "An integrable model of quantum gravity", Physics Letters B356,
211-216 (1996)

D.Korotkin, H.Nicolai, "Isomonodromic quantization of dimensionally-reduced gravity", Nuclear
Physics B475 397-439 (1996)

D.Korotkin and H.Nicolai, "Separation of variables and Hamiltonian formulation of the Ernst
equation"
, Physical Review Letters 74, 1272-1275 (1995)

H.Nicolai, D.Korotkin, H.Samtleben, "Integrable Classical and Quantum Gravity", in "Cargese
1996, Quantum fields and quantum space time" 203-243 , Plenum Press (1997)

D.Korotkin, H.Nicolai, H.Samtleben, "On 2D quantum gravity coupled to sigma-model", \The-
ory of Elementary Particles", eds. D. Lust and G.Weigt, Nuclear Physics B (Proceedings Sup-
plement) 49 1-10 (1996)

Lecture Notes


D.Korotkin, "Introduction to functions on compact Riemann surfaces and theta-functions", in
"Nonlinearity and Geometry"
, ed. D.Wojcik and J.Cieslinski, Polish Scienti¯c Publisher PWN
109-139 (1998)